Hmm. So what about a 30 to 50 minute run wearing sweatpants / hoodie?

I believe that heavy exercise can also increase heat shock proteins, but don't quote me. This info is all readily accessible online.

I doubt high heart rate is a good mix for high temperature, you want them to balance out, see also homeostasis from high school biology.

I'm thinking more like, when I run with a sweater and heavier sweatpants, but the time I'm at the 5km mark I'm seriously sweating. So, not just higher heart rate. I'm talking "feels like a fever" heat, for 20 minutes, a few times a week.

But I run with my heart rate low, I don't like exceeding 150 on these runs.