There is a process.
If you're going to transfer your Betta to a tank with a different temperature it's best to have him in a temporary holding vessel of some kind, and gradually pour water from the new tank (the new temp) into the vessel, then finally he goes into the new tank after he's had time to adjust to the new temp.
Bettas are pretty sturdy and resilient but I still make sure I do this when I do his water changes, even tho his temporary holding spot (a big beer mug I bought especially for the purpose) probably doesn't change temps much while he's sitting there during water changes.
Also what I said earlier about heaters and small tanks, I noticed that my inexpensive heater with no dial or control has a self-adjusting feature that turns it off when the water reaches 28*C and kicks in when it dips below 26*C, so if the water gets too hot it might not be the heater(?), its just that the room is too warm or something perhaps.