Read the manual.  Some amps have forced air cooling for full performance
with under-seat mounting.

3 of my 4 amps are mounted under the passenger and driver seats and after
many years I have experienced no ill effects.  The fact that it is a Class D
means that it will operate more efficiently and (in theory) operate cooler
than regular Class AB amps as less power will be converted to heat, so I
would think there would be no problems at all with under seat mountings, as
long as there is at least SOME space for air to circulate over the amp (just
a couple inches should be adequate).  If it is a forced air-cooled type
(with a fan), then make sure the air-intake vents are not blocked.  Also, as
already suggested, consult the manual as you don't want to do anything that
might shorten the life of your amp OR invalidate the warranty.

MOSFET

if you have a tall amp and short space under your seat I wouldn't do it.
I'd give the amp a couple inches on top so it can get at least some
airflow.  otherwise it'll be fine.  I put a class A/B amp under my
dad's F150 seat and I've never seen nor heard of it shutting off, and
A/B amps are less efficient than D so they should produce more heat.

I have my class d sub amp mounted vertically on the box in the trunk,
between the box and the back seat...  I run that amp often and hard;
and there's not a whole lot of space back there.  I was so concerned
about this that I mounted a fan and a custom-designed-and-made
temperature sensor on/near the amp.  Truth be told; it looks really
cool, but I haven't had to use it yet - and my manual specifically said
that my amp should be mounted flat (which it's not) for cooling
purposes...  You can check it out here:
http://www.cardomain.com/ride/2367650
The moral here is that (at least for the model I got) you don't have to
worry about overheating a class d.
~Mister.Lull