does the thunderbolt display have a cooling fan? My recently purchased 27" Thunderbolt display is overheating. Is there an internal fan that should be coming on?
Yes, the Apple Thunderbolt Display does have a fan.  See: Apple Thunderbolt Display Teardown

It's a brushless fan, so it might be rather quite when running at lower speeds.

I have a Thunderbolt Display and I can't recall having heard it as I usually hear the fan from my MacBook Pro above all.

Cropped image from link above: