With regard to the sub-question about measuring temperatures at some distance from the probe, the answer is a qualified yes; see below. Measurements made essentially in contact with the thing of interest, such as measuring the temperature of atmospheric gases with a sensor in contact with the gases, are called "in situ" measurements. Measurements made at a distance by means of something, usually electromagnetic radiation of one sort or another, propagating from the location of the thing to the location of the sensor, are called "remote sensing" measurements. You're asking if there are any remote sensing techniques that could be applied to the atmospheric entry probe, right?
Indeed there are, but you sacrifice both accuracy of the measurements and a lot of the mission's instrument mass allocation. The technique most often used for remote measurements of temperature is infrared radiometry. Or you might use microwave radiometry, if you're measuring really low temperatures. But this technique is most useful for measuring temperatures of solids. At infrared wavelengths most solids have emissivities very close to unity, so they behave pretty much as blackbody radiators. If you measure the intensity of the blackbody radiation being given off by an object at multiple wavelengths (at least two, preferably more) the shape of a blackbody spectrum will tell you what the temperature of the object must be to fit the pattern of the measurements.
As an example application for measuring the temperatures of solids, inexpensive hand-held radiometers that use this technique are commonly available in hardware stores. I have one at home. They are definitely cool, definitely useful when the home air conditioning is doing something wierd, and are moderately accurate. Note: they are not very accurate! For various materials the infrared emissivities do vary a little across the IR band, and this affects the assumption of an ideal blackbody radiator. So with one of these devices you can get temperatures typically accurate to 1 or 2 C, but not 0.1 C.
Remote measurements of temperatures of gases is a whole different ball of wax. The emissivity spectra of gases are wildly non-blackbody and are very different for different gases, so the assumption of a blackbody spectrum is invalid. It is possible to make radiometer measurements of IR intensity and infer the temperature of a mixture of gases, if you know exactly the composition of that mixture of gases. If you do know that composition, then you can make the radiometer measurements at carefully chosen wavelengths and back out the temperature. But the radiative behavior of gases is somewhat akin to the conductivity behavior of semiconductors: it only takes a tiny amount of something to change their behavior tremendously, especially at a single wavelength. So if you're trying to make radiometric measurements of a giant planet atmosphere's temperature, and you assume all the usual constituents in that atmosphere (hydrogen, helium, methane, water, ammonia, hydrogen sulfide) but if it turns out there's also a bit of phosphine, or carbon monoxide, or hydrogen chloride, or some such, then the radiometer's calibration is no longer valid and you can't trust the inferred temperatures. All it takes is one unexpected constituent in the atmosphere, with an IR emission line on top of or near one of the ones the radiometer uses, to drive the uncertainties in the retrieved temperatures through the roof, making them useless.
Another reason to use in situ measurements on an entry probe is that they are very low in mass and power use. Radiometers are more massive and use more power, and those are precious commodities on an entry probe mission.
If some of the science objectives you're trying to achieve at a planet are of such high priority, and are so difficult to do remotely, that you're sending an entry probe to do the required measurements, then in situ measurement of temperatures is the hands-down winner in that trade.
The NASA Deep Space Network uses a microwave radiometer at its big ground stations to measure not the temperature of the local air, but the amount of water vapor in the local air. The amount of water vapor in the air affects its refractive index, and this makes a difference in measurements of the distance to spacecraft they are tracking, of concern especially when they are trying to measure the gravity field of the planet where the spacecraft is. This kind of water vapor measurement is possible because we know the composition of Earth's atmosphere to a gnat's eyelash, with the primary variable quantity being water vapor.