A really mad idea. But I like it.
Don't worry about how to fit it for now. By the look of the snap shot the unit will fit with a little modding of the case. Think about the power it requires and the connectivity, both power and connections to the sound card. As far as I know you can connect the audio, digital/analogue, from CD drives to 'audio in' connections both on the mobo and sound cards. So as long as the head unit has pre outs you'll be able to use these. For in computer power amplification you'd have to connect the output from the sound card to the input of the head unit for the output to appear at the speaker plugs on the back plate. Now if the head unit has power amplification then your gonna need a hefty power supply. These units can draw in excess of 20 Amps from a 13 Volt power supply. I'd recommend keeping the power supply to the Head unit and the computer completely separate.
The Power Amp idea is the way i'd go personally. Although both are really cool ideas.
Heat? Well there's plenty cooling options out there.
This will be interesting....