Those kind of temp swings aren't healthy for anyone.
When the temperature drops even by a lot, I'm usually fine, but going the other way is hell on my sinuses. On Sunday the high was about 18. Yesterday, it rained and hit 45 degrees before noon and slowly went to about 27 by midnight. Overnight the bottom seriously dropped out and it's 5 degrees outside.
Yesterday, my head was on fire all day long. The headache would lessen a bit with Advil but it never went away. When I get a sinus headache like that, it will often trigger a migraine that will then last for another 2-3 days.
This morning, though, my head is fine. I am obviously not claiming that the temperatures are all to blame (or credit), but it's definitely a pattern that I've noticed over the past 10-15 years. When weather fluctuates like this, my head is affected on the upswing but not when temps drop again. I figure it's more about barometric pressure than temperatures. Either way, when I see those kinds of swings on the weather report, I brace myself!