How many watts will this amplifier need to dissipate?

scswift:
Of course this also assumes I am running the amplifier at maximum power with something approaching a square wave at full volume. But it's best to consider the worst case.

If it's a class D amplifier then the waveform and volume level won't make an awful lot of difference.

Class D uses PWM to generate the output waveform. MOSFETs only heat up when they're in transition from LOW<->HIGH. The number of transitions per second doesn't vary with the signal being amplified.

So...you have to assume full power dissipation at all times.