Can we mount a TV over a fireplace with the chimney directly behind it?
When in use, the chimney itself will be at a higher temperature than ambient. Just how high will depend on several factors: materials used, thickness, fire heat output, etc. You can get an idea of just how hot just by touching the visible part of the chimney with your hand, and a more precise reading from an IR gun. This is actually a desirable feature, since the chimney radiates heat into the room.

On the other hand, the television is electronics. The individual components radiate some heat (flat-screen give off less than old cathode-ray tubes, but still), but do not like to work at high temperatures - which is why you will find heat sinks on some components and air vents all around the back of the television set: to get some air moving and cooling the electronics inside.

So, in the first place putting the television on the chimney is probably not a good move for the set itself. The manufacturer may or may not specify in the documentation just how much ambient heat is acceptable, but as a rule of the thumb anything above 40C (about 105F) is a no-no, will void the guarantee and shorten lifespan. Unless it actually starts melting the plastic ... and please don't laugh, I have seen it happen.

If you do decide to proceed, I would make sure to use some isolation. If you use plastics or foams, make sure they can stand the heat. Otherwise, just leaving a separation or air gap between the set and the chimney wall may be enough to isolate the television from the heat. 

Also take into account any metal fixtures you use to actually bear the weight of the television. Since metal transmits heat, you should try to reduce their section (while still being strong enough for their purpose). Steel would be better than aluminum, and much better than bronze or copper (steel conducts less heat).

HTH.