"Hundreds" of watts is a bit of an exaggeration, but around a hundred is possible. Still WAY too much for a plastic head.
It looks like SL's LED head has an aluminum body, which should help loads with keeping the LEDs cool. If you want it to last a good while, that's a lower limit than melting the plastic.
Given that big aluminum body, it seems surprising they only pull 540 or 615 lm from it. Their HL looks like the front half of the head is aluminum too, instead of rubber, and the back looks to have deeper fins. That might give it 3-4 times the surface area, but they claim nearly ten times the light output! That suggests the thermal design of the non-HL heads might be a compromise, or maybe the HL is over-rated, or maybe a bit of each.
At any rate, I doubt you could do better in a plastic head than SL did in a (half) aluminum head. If you run the numbers, 540 lm at 140 lm/W is 3.86W of light. 140 lm/W is around 38% radiometric efficiency, depending on spectrum, so total power input needs to be just about 10W, and heat is over 6W. Somewhat higher, as some of the light generated by the LED doesn't escape the light and gets converted back to heat. I'm not good with plastic, but it seems that even if you spread it around pretty well, 6+ watts in a sealed plastic box is going to get hot.
For reference, any idea what the halogen puts out?