Is it because the amp gets too hot and it will overheat (i imagine that is more of a tube amp problem) or does it damage the speakers?
Well its common sense really, Tube amps can handle heat (Obviously) but SS amps are different. And the answer to this, Just dont leave it by a heat source! Problem prevented!
Does heat damage the speakers though?
Unless it sets on fire, or something melts, I can't see how it would. But it's easier to just leave it away from the heat source, rather than putting it next to a radiator just because you can.
Possibly, not 100% but it could mess up the gluey stuff! lol
Well I live in a dorm room and I have a B-52 AT212 and I don't really have anywhere else to put it but near a floorboard radiator that stretches across the entire room.
Tube amps can get hot, it's not recommended to have them up against a wall soaking in it's own heat. You definitely don't want it on top of a radiator. As for the speakers, I'd imagine a lot of heat might shorten the life of the cone. But that's just speculation.