I had the same issue. I have a similar bowl to yours and found this great heater at Wal-Mart.
It keeps my tank at a steady 78-79 degrees 24 hours a day and my betta loves it and is a lot more active because of it.
The box says 2-5 gallons or something but it works great in a 1 gallon as well. It's only like 10-15 dollars depending on which walmart you go to.
Good luck! Also, if you're going to install the heater take him out, let the water heat up, and then float his bag in the water to let him get used to it, then let him out. So you don't shock him. :)