Depending on what size amp you choose, you should have no problem, and there is plenty of airflow under there. but if you ever put subs in your car it will be a PITA to get your RCA's and power wires back in the trunk and under the seat.
FYI if your not into super systems a great budget setup is a 5 1/4 component set with 35.X 2 rms amp. only amping out the front and let the HU amp out the rear.
I would have to agree here. Heat rises and the bottom of the seat will be close to the amp. And it will tend to get hotter down there. Put in trunk. Peace. That's where mine is including all wires. Peace.