If he is swimming normally now not laying on the bottom and if he ate (not sure when his feeding time) than i hope he is fine.
Not sure what happened though...I always afraid about temperature difference too. I had accident one time. I forgot about temperature and change my betta. The difference was like about 8*. So he was kind of a little lethargic. Since than i let water sit for 24 hrs . I have 2.5 gall so it easier for me. Then 30-40 min before i change my tank i make another .5 gall with warmer water. Then when i change it i mix cooler water with warmer. It works for me. And when my house warm and i don't use heaters then it even better and very convenient you just using aged water and it the same temp that your betta already in. This way you don't shock them with temp difference.
Also very convenient to have stripe thermometer which you can stick outside on your tank and see temp while you pouring the water in. Those thermometers $3-4 and very sensitive it so convenient.
So is he ok now?