In fact, the receptacle (from the extension cord I'm using) doesn't "feel right" anymore. The two flat holes aren't exactly parallel, perhaps from continuous, abnormal heating inside.

On the same circuit, a previous smart plug I was using heated up so much that the case cracked, which would point towards a hardwired receptacle issue.

> Our bathroom has no heater, but we leave the door wide open when not in use, and convection takes care of the rest. If you are habituated to keep the door closed, question that habit.

I'd gladly do that, but the layout is such that the bathroom is a dead end and no significant heat gets in. In fact, quite the opposite when I need to open the kitchen window. thanks for suggesting, though.

In short: 
Check hardwired receptacle for loose contact, replace as needed
If OK, check for screws not tight enough. Tighten or replace as needed.

EDIT:
actual picture of extension cord.[![Heavy-duty extension cord][1]][1]


Picture of oven plug (same circuit as the heater, but never on at the same time)
[![Oven plug (replaced)][2]][2]


  [1]: https://i.sstatic.net/df1Ow.jpg
  [2]: https://i.sstatic.net/2kSLl.jpg