Last-ditch efforts to maintain thermal homeostasis

I was in the gym's steam-room today and a thought occurred to me: have I truly thwarted all possible mechanisms for maintaining thermal homeostasis?

There's sweating, which is thwarted because the steam-room's atmosphere is as close to 100% humidity as possible, so there's almost no evaporative cooling.

There's convection, which is thwarted because the ambient temperature is above normal body temperature.

And I can't get rid of heat by exhaling, because every lungful of air I inhale is already above normal body temperature.

I think that, eventually, I should go into hyperthermia, but beside the above, are there any other last-ditch attempts to lower core temperature that my body could take?