...any idea how they like heat?
The casing is stamped metal, but it's a plastic dome, I suspect it would be ok though you never know. The HTD of ABS I think is above 200°F, but then again this dome may be LexanŽ or PolyCarbonate, both of which have higher HTD's. Even if it got soft, it would still be supported by the metal frame, I wouldn't worry about it, if you can keep it towards the intake side- look at all the other plastic in your engine bay.
82 fj40, 99 uzj100, 06 gx470
97 DR650, 05 525EXC, 01 XT225, 89 TW200, 09 TTR125, 07 TTR90, 07 CRF50