How many watts will this amplifier need to dissipate?

scswift:
While I'm inclined to agree with you because what you said earlier seems to make sense, if that's true, then how do you explain the efficiency vs output power graph in the top center of page 8 in the datasheet:
http://datasheets.maximintegrated.com/en/ds/MAX9744.pdf

Good question.

I'm guessing it's something to do with where it says "...with an inductor in series..." at the top of the page.