Does anyone else feel cold/chilly around the start of their cycle?

For awhile now, I have noticed I will feel chilly every time my period starts, and it has nothing to do with the temperature outside or inside. Believe me, it is still hot here (no sign of fall). The AC is on, but we keep it fairly warm inside, 74 or 75F. I definitely don't have a fever or feel sick beyond the usual period complaints (cramps, backache, etc.)

I started my period today (well, I think it's going to start as I'm spotting), and whenever the AC kicks on, I am absolutely freezing. I'm even a bit chilly when the AC kicks off. I feel like turning the heater on and it's 90F outside!

What's up with this? I don't remember this happening when I was younger! I'm 46 now.