I woke up this morning and went to go feed my betta fish. He ate the usual, and nothing seemed different until I took a closer look at his fins. The edges seem a tiny bit ragged and are starting to lose color (grayish see-through color now instead of blue). It's barely anything, but I'm starting to worry.

If this is fin rot I think I have a theory of why this happened. He lives in a small tank with no gravel in my room. My room isn't the best room ever - it gets super hot in the summer and super cold in the winter. Where I live we are experiencing a heat wave, and the heat could have stressed him out.
I moved my betta fish to my sister's room, where it is much cooler, but still the right temperature for a betta fish.
Also, if this is a case of fin rot, I don't think it was caused by an unclean tank. I clean it every 4 days and I'm starting to do partial water changes every day to keep the water from getting too warm again.
Any advice?