Okay I know it's weird to reply to a comment after 2 years, but I actually have an answer for this now.

According to a friend of mine with EDS, she thinks it's very likely I have something similar going on, though maybe at a subclinical level. One of the lesser known effects of that is temperature sensitivity, so, that's probably part of the puzzle in my case.

Caveat - I haven't been able to find a doctor for a while, so I haven't actually been subject to any examination or diagnosis.