Post this in the Audio forum, you might get some more qualified answers in there. Actually, maybe a moderator can move it there for ya.
To answer your question: I think there WILL be heat issues if you don't take the necessary precautions.
BUT, if you get an amp that is way overpowered for your system, that is a different story. An amp heats up when it's being pushed, so if you don't push it, it shouldn't be a problem if you can fit it in there. For example: if you are looking to add "some" bass to your system and have an 8 or 10" 2ohm sub that can handle say 200wmax, then an amp that pushes out 1000w at 2ohms will not get hot if it's only using 20% of it's rated amplifying ability.
If I were you, I would take these steps:
1) make darn sure there isn't a better location to mount the amp (under the rear seat is the last resort)
2) get a more powerful amp than what is needed.
3) amp has a built-in fan.
4) amp has an over-temp sensor and will shut the amp off when it overheats
5) maybe see if you can build a "cage" of some sort around the amp so that the top/sides of the amp housing do not come in contact with the carpet.
That's about all I can think of....I have an amp mounted underneath each of the front seats and have no heat problems because there is at least 1-2" of air between the seat bottom and the top of the amps, plus plenty of air circulation around the amps. Did you look at those locations?
Hope that helps.