The Earth's thermopause is varying greatly between 500 km (310 mi) and 1000 km (620 mi) altitude. If a craft orbits inbetween these altitudes, or reaches them at some point of their orbit, is there any possibility to determine if it's still in the thermosphere or in the exosphere already? Has this been done? Other than high LEO satellites, examples would include the Space Shuttle flights to Hubble and some Gemini missions as well as the Apollo moon flights.
One option how to determine it might be if a sensitive enough instrument measured a reduced microgravity due to reduced atmospheric drag. The ISS experiences about 3 micro-g due to air drag; I guess there is some value that might determine the exobase from where molecules no longer collide with each other, except by chance.