During the launch and re-entry of the Space Shuttle, what are the measured and estimated temperatures (or distribution) of the shuttle nose cone as a function of altitude? How is the temperature measured (at the cone) and what is the uncertainty or alarm limits?
The trajectories are quite different between ascent and entry. Launch trajectories are designed so that the aeroheating is very little. Entry trajectories, without the advantage of minutes of powered flight like ascent, cannot avoid significant aeroheating. This aeroheating is several orders of magnitude more than ascent.
The temperature of the heatshield can be estimated by its radius of curvature, the dynamic pressure, and airspeed. Complicated computational fluid dynamics models, anchored by test and flight data, estimate what the temperatures will be at various points across the surface. Monte Carlo simulations provide engineers a distribution of the temperatures, given small changes such as with the vehicle's trajectory, attitude, heatshield surface roughness, and aeroheating model parameters.
It is common that the first several flights of a new vehicle will instrument its heatshield to validate the aeroheating models used for its design. This instrumentation is typically thermocouples. The uncertainty is dependent on how well the instrumentation is built and integrated into the thermal protection system, and how well it is calibrated.
A good summary of the experience in building and using heatshields, written in the early 1990s by NASA, may be found at https://ntrs.nasa.gov/api/citations/19930003261/downloads/19930003261.pdf.