How many watts will this amplifier need to dissipate?

That's... counter-intuitive. At first I thought you must be wrong, because the duty cycle has to vary to vary the power into the speaker, but it doesn't really matter what the duty cycle is, does it? As long as it's greater than 0, if the PWM freqeuncy is 300KHz, which it is for this chip, then the mosfet will transition from high to low 300K time a second, regardless of whether the duty cycle is 5% or 95%. All that varies is how long in that period it is in the on or off state.

Interesting.

That raises more questions than it answers though, in regards to heat dissipation. That would mean that at 12V into a 4 ohm load, regardless of how loud the music is, I'm going to dissipate 5W. But that seems to be more than...

Wait...
?JA, Single-Layer Board................................................37°C/W

That's JA, not JC. That's the temperature rise if the chip is only dissipating power through the air surrounding it.

It must be able to dissipate much more heat directly through the heat sink into the PCB. But where's the JC rating? And why does that rating specify that it is for a single layer board, if it's the rating for dissipation to ambient air? And why is there another rating for JA for a multi layer board? None of this makes any sense.