Bettas do 'sleep' and find places to 'rest'. So, as long as he isn't always doing that, but only doing it periodically for 'rest', then I wouldn't worry about it.
The thermometer is reading about 26.5 C/80 F.
I was asking because I know that male bettas kept at 'traditional tropic' temps (72F - 75F)are more susceptible to fin rot. Typically, 80F is what I would recommend as a 'safe' temp.
If you are concerned about this, I'd suggest starting a new thread in this section. We have a few very knowledgeable betta keepers around who will be happy to give you some assistance, but may not check this thread specifically. I'd title it something like: "Is this fin rot?" or similar.