That's not important at all; what's important is that black body radiation has a fixed maximum flux -- its spectrum or lack of coherence isn't why you can't hea

That's not important at all; what's important is that black body radiation has a fixed maximum flux -- its spectrum or lack of coherence isn't why you can't heat another body to a greater temperature. It comes back to etendue, or if you prefer the 2nd law. You could reproduce any fixed black body spectrum (to arbitrary accuracy) from a set of thermal sources and filters (or a set of lasers, LEDs, etc. with random phases) to arbitrary fluxes just like a laser has, and use this light to heat objects to arbitrary temperature. But if the original emission is of black-body type, you cannot -- the flux is given by the quantum mechanical process and a function of local temperature only. From then it follows from etendue conservation you cannot achieve higher temperatures.