The determination that Venus has a hellish surface is a great example of scientific detective work and its close association with technological advances that allow better and better measurements.
In 1952 Harold Urey had argued that with a roughly Earth-like atmospheric density (postulated, not measured!), its position orbiting ~0.72 AU from the sun should make its average surface temperature somewhere around 53 C (326 K, ~127 F) [H.C. Urey, On the Early Chemical History of the Earth and the Origin of Life, Proceedings of the Nat'l Academy of Sciences of the USA, Vol 38 #4, pp.351-363, Apr. 15 1952]. Others proposed even cooler temperatures. NASA's final report for the Mariner 2 mission to Venus (look out, that's 360 pages!) begins with a summary of what was known before the Mariner 2 mission's observations, stating "Observers have visualized Venus as anything from a wet steaming abode of Mesozoic-like creatures, such as were found on the Earth millions of years ago, to a dead, noxious, and Sunless world constantly ravaged by winds of incredible force."
The scientifically-based detective story begins in the 1950's with ground-based (Earth's ground, of course!) radio astronomical observations, where you point a big dish antenna at a planet and measure the intensity of the radio energy the planet is emitting. Often you measure not just at one frequency but at multiple frequencies, or a continuous range of frequencies, to get a radio spectrum. If you assume the body emitting the energy acts as a black body, then if you know the projected area of the body (as seen through the radio telescope) the intensity of that energy at a given frequency can be translated to the body's effective black-body temperature, called its brightness temperature. The process of translating measurements to inferences of other physical parameters is called data reduction, so in the literature you often see references to "measured fluxes reduced to brightness temperatures". If you have spectral data whose wavelength dependence is like a black-body spectrum, you can derive an effective temperature without knowing the body's projected area. In the 1950's antenna technology got to the point they could build parabolic reflectors for dish antennas big enough, and receivers could be sensitive enough, to detect radio emissions from the terrestrial planets. Nowadays we have antennas large enough, and interoferometric techniques sufficiently mature, that radio observatories can resolve planetary disks into many pixels, resolving spatial variabilities in the planets being observed, but back then you received radio emissions from the entire Earth-facing side of the planet all at once; one pixel.
This source provides an excellent summary of the early ground-based measurements and the puzzles they posed. Along with the Wikipedia article, they provide good general references for this question's topic, and most of the summary that follows.
Mayer, McCullough, and Sloanaker made the first successful radio astronomical observations of Venus in 1956; they published reports that year in the Proceedings of the IRE (Institute of Radio Engineers; this publication was subsumed into the Proceedings of the IEEE in 1962) but I can't find the paper itself online. In 1958 they published more extensive results, including radio fluxes at 3.15 cm wavelength reduced to blackbody temperatures around 600 K. In the appendix they report additional observations at 9.4 cm giving a temperature of 740 K, very near the current estimate for temperatures at Venus's lowlands, which constitute most of the planet.
This contrasted with the measurements at millimeter wavelengths by A.D. Kuzmin that showed brightness temperatures near 300K, and a spectrum that looked nothing like a black body. Scientists came up with two ways to produce this spectrum (two prime suspects! ;-): 1) the surface is hot, but at shorter wavelengths the atmosphere becomes opaque, so observations at those wavelengths are seeing radiation from higher in the atmosphere where it is cooler, not from the surface; 2) the surface is cool, but processes in the ionosphere radiate strongly in the cm-decimeter range of the radio spectrum, making it look hot at those wavelengths. Both of these models could fit the spectrum, so no reliable conclusion could be reached regarding which model was right (which suspect was the one we're after). Optical spectra had indicated the presence of $CO_2$, so in his 1960 doctoral dissertation Carl Sagan supported the hot-surface model, proposing that the $CO_2$ greenhouse effect could contribute to high temperatures in the lower atmosphere and at the surface. The one sticking point with the hot-surface model was that to get enough atmospheric opacity to make the short-wavelength observations 300 K cooler than the cm-wavelength observations required atmospheric pressures in the 20-100 atmospheres range. At the time scientists took the view that The pressure of such an Earth-like body can't be that high!...(...can it??...) so they didn't quickly adopt Carl's suggestion.
Ground-based radio astronomical measurements in 1962-1964 used new, larger dishes and new techniques such as interferometry that allowed higher spatial resolution. These lent some support to the hot-surface model when they detected limb darkening at Venus at ~3 cm wavelength (although that source refers to stars, the concept of limb darkening applies to planets and other bodies too). A month later the Mariner 2 spacecraft, using an instrument that was essentially a radio telescope, just placed a lot closer to Venus, also measured limb darkening at 1.9 cm wavelength. But a Caltech ground-based interferometer operating at 10 cm wavelength observed limb brightening, leaving the scientists scratching their heads and wondering What the...heck???
(Aside: about this time scientists began making radar observations of Venus, using the NASA Deep Space Network's largest antennas and the huge Arecibo facility (both a radio and a radar telescope). A radar telescope transmits a very strong signal to the target body, somewhat akin to illuminating an object with laser light, and then receives and records the reflected signal. Soon after, Stanford University built a dedicated radar telescope in the hills above the main campus. These radar systems were able to begin the mapping of surface features at Venus, and reliably measure for the first time Venus's rotation rate.)
Astronomical methods of the time had achieved all they could do regarding the problem, so this dichotomy of two competing models (two prime suspects) remained until we actually got there with better instruments and techniques.
After Mariner 2 scientists knew solving the puzzle would require new techniques and instruments. At Stanford, scientists and engineers had developed the radio occultation method (Prof. Von R. Eshleman was my Ph.D. advisor!) for measuring vertical profiles of atmospheric pressure and temperature. This technique involves flying a spacecraft behind the destination planet as seen from Earth. Just as a spacecraft is starting to go behind the planet ("immersion") or as it's coming out from behind the planet ("emersion"), the radio signals traveling between the spacecraft and Earth pass through the planet's atmosphere. Careful reduction of the phase, Doppler shift, and amplitude of the resulting signals provide these vertical profiles, and more. The same observations can characterize the electron densities in a planet's ionosphere, and detect radio-absorbing constituents in the neutral atmosphere.
Mariner 5 performed a radio occultation experiment at Venus. Preliminary results (abstract only, the full paper is behind a paywall; full reference is: Atmosphere of Venus as Studied with the Mariner 5 Dual Radio‐Frequency Occultation Experiment, G. Fjeldbo, V.R. Eshleman, Radio Science Vol. 4 #10 pp 879-897, October 1969 DOI: 10.1029/RS004i010p00879) concentrated on the ionospheric results, but did show that at ~35 km altitude the signals reached critical refraction. Critical refraction is where the refractive curving of the signals' ray paths is so large that any horizontally-traveling signal at a lower altitude has its radius of curvature smaller than the distance to the center of the planet, so the signal is effectively trapped within the atmosphere. So, unfortunately, the radio occultation method couldn't probe deeper than that. But what they did see from preliminary data reduction verified that temperatures were zooming with decreasing altitude, and the pressure at 35 km altitude was already high, nearly 10 atmospheres. This strongly argued for the hot-surface model.
In Oct. 1967 the Soviet Venera 4 used the atmospheric entry probe technique to directly measure atmospheric temperatures, pressures, and composition. It wasn't designed to handle pressures as high as it encountered so it made measurements only to 26 km altitude, but its results were consistent with the Mariner 5 radio occultation measurements: at 26 km altitude the temperature was 262 C (535 K) and the pressure 22 atmospheres. It also made the first direct measurements showing that Venus's atmosphere was overwhelmingly $CO_2$ with a few percent of $N_2$ and only traces of anything else, notably water. That much $CO_2$ makes for a powerful greenhouse effect. Atmospheric physics dictates that as you go lower in the troposphere it will only get hotter, and the pressure will only increase. Atmospheric models using the equations of atmospheric behavior were now predicting surface temperatures of 600-800 K and pressures of 90-100 atmospheres, and these were considered reliable: scientists then accepted that Venus's surface was a good model for Hades.
Those observations laid to rest the notion that the surface of Venus was like a very hot tropical jungle, i.e. the cool surface model. Hypothesis #1, the hot-surface model, was convicted. It was sentenced to be bandied about seemingly endlessly in professional journals, the popular media, etc.
(Historical note: At first the Venera 4 team claimed that they'd made measurements all the way to the surface, so the 262 C was a surface temperature. It didn't take long for scientists and engineers to figure out that the probe's radar altimeter had suffered from altitude aliasing, and its deepest measurements were actually from 26 km altitude.)
In 1971, armed with the Soviet Venera 4 results in addition to the Mariner 5 results, the Mariner 5 team published a more comprehensive paper. (Again, abstract only/paywall; full reference: The Neutral Atmosphere of Venus as Studied with the Mariner V Radio Occultation Experiments G. Fjeldbo, A. Kliore, V.R. Eshleman, Astronomical Journal Vol. 76 #2 March 1971 DOI: 10.1086/111096) At 35 km altitude the temperature was 500 K (227 C) and the pressure ~9 atmospheres. Extrapolating their profiles to the surface indicated a surface temperature of 775-800 K and a pressure of 90 atmospheres (~91 bars), though they noted that if the temperature lapse rate observed in the 50-35 km altitude region changed below 35 km the surface temperature could be different.
Indeed that lapse rate does change, and the current accepted values for the average temperature and pressure at Venus's lowlands are 735 K and 92 bars. But the measured temperatures and pressures above 35 km agree well with subsequent in situ and radio occultation measurements. The radio occultation measurements turned out to be very accurate.