It is possible to estimate the temperature from the ratio of Stokes and anti-Stokes bands in Raman spectroscopy. So if you would have a Raman microscope capable of measuring also anti-Stokes (i.e., with a suitable filter), then you should be able to get temperature information with the resolution of several microns. I would advise you to check related literature and see what are the limitations and also the accuracy of this method. I have no direct experience with such measurements, so I can´t provide you with all the necessary details.
Thanks everybody for the helpful answers! I was aware of Abbe's Law but did not consider the wavelength of thermal radiation at ambient or slightly elevated temperatures!
Thanks for pointing that out!
Josef, thanks for the Raman Microscopy answer. I read a little about it and it sounds doable. I will search appropriate equipment on campus!