This is no more odd than my mother’s family’s belief that sleeping in front of a fan causes illness & stiff muscles.
"Stiff neck" 'teekert mentions and "ear pain" would be mentioned as dangers of draft too. It's so pervasive in the local culture that I even have to occasionally remind people from my generation that common cold is a virus, not a side effect of exposure to elements.
When you're contaminated (and you don't know because you don't feel it yet) you shouldn't stress your immune system with additional stuff like the temperature differences between different body parts. Why do you want less of blood circulation in the contaminated areas?
What is called "extreme hot" for North or East Europe is a pretty normal temperature for human species anyway.
What is called "pretty normal temperature for human species" is barely bearable for me, and has been so since I was a kid. It completely destroys my productivity.
I recall reading here that the "productive" temperatures fall into the range I consider comfortable, so I must not be too much of an outlier.