Here is a cheap tank that is 2.5 gallons you can buy for your betta and you can get nice tanks for even cheaper. This one even comes with a filter, same one I have in my tank that works great. You can get heaters from wallmart for like $14 and silk plants are pretty cheap if you buy the three pack which they also have at petco. Walmart has cheap drift wood caves too.
This tank has very nice light settings as well for night time.
This tank is a 1.8 and made by the same company. It's still a very nice tank and a little cheaper than the 2.5 tank.
Also heaters never heat above what they are set at. Betta's need a temp between 78-84 to be really happy and healthy. Some heaters like the $14 one at wallmart are preset to 78, when the water temp rises above 78 it shuts off and when it drops bellow 78 it turns on and has worked great in tanks under 5 gallons.
Even if the water looks clean the tank could be toxic from ammonia. Anything over .50 ammonia is fatal to fish. If you can buy an ammonia liquid API water test kit you can test the water to see where it's at.