Removing the top module is indeed possible, you can continue to use the FP3 without it. In fact, the FP3 can be booted and used – to a very limited extent, of course – without all four small modules (I tested this). I’m not a technical expert, however, “the receiver” sounds like something you might not be able to do without.
I actually wondered myself about heat emission from the LED. In general, I would guess it’s low (compared to light bulbs). When you disassemble the FP3 and have a closer look at the top module, you might be able to estimate better how far away the actual LED is from the surface of the module and how much additional distance to the display glass there is. If most of the distance is inside the top module, a cover might not make such a difference. It seems that a 2-3 mm round spot (that doesn’t cover the two other holes) would be enough.