I understand how infrared thermometers work or how you can look at something’s radiation and tell it’s temperature from the black body radiation curve.
But all the above thermometric methods require the thermometer to be cooler than the surrounding.
If I understand, locations like the center of the sun or the early universe is/was homogenous (that is the temperature was the same everywhere). In locations like this, is it thermodynamically possible to measure temperature and how ? The thermometer has to be inside the system and has to provide instantaneous readings.
You could use the ideal gas law. Though that just shifts the burden to creating a low-pressure zone to compare the pressure to, instead of a low-temperature zone to compare the temperature to (I assume you have some way of getting the count of the gas particles).
I’m not sure what limitation you are referring to. A conventional thermometer sitting in homogeneous air or liquid will read the temperature correctly, without any access to any external heat sink.
Yes, of course, defining the problem & constraints more clearly would change the answer.