I would be more concerned about hypothermia and the possibility of frostbite than I would about heat stroke. -10 isn't super-cold, but with only underwear to protect me it'd still be quite dangerous. The parka, on the other hand, still leaves the legs and head available for dumping heat via sweating and if all else fails I can hose myself down with additional water to help with that. It will be miserable but I doubt I'd suffer any long-term damage.

I wonder if a parka might be a relief when it is extremely hot out? It might protect you from the heat like a sheep's fleece or camel fur.

Only one way to find out for sure...

I think hosing yourself with water is cheating.

I'll take the wear a parka. But I'll just tie the arms around my neck like a cape. Doesn't say how you have to wear it. No clothes underneath! Only parka cape!