Underseat amp installation viability

I noticed a seeming dearth of dead space under the rear seat near where the battery goes. Would I have any serious heat issues to worry about by stuffing my 600 watt JL audio monoblock and 400 watt 4-channel Xplod under the seat so I can have a less cluttered trunk? Has anyone tried this before (search tool says 'no')?

Mine has always been mounted in the trunk (Orion HCCA D1200 mono. The old school BOOMER). I never got brave enough to try mounting under there. There is absolutely NO airflow under the seat. I'm assuming that any amplifier would have a bad day in the middle of summer while getting pounded if it were under the rear seat.