Neil D is correct, a heater and tank are healthier for your betta.
Smaller betta containers need more water changes (at least twice a week) because the tank has no filtration. Lack of stable heat stresses the betta as well.
When you are ready to put together a new set up, you will need to 'cycle' the tank (before the fish goes in, btw). You can read up on cycling on this forum.
Also, be sure to buy an adjustable
heater. That way, you can adjust the temperature of the water to the tank size and room temperature (some places on Earth get mighty cold in Winter, and it can drop the room temperature - which drops the tank temperature).
Buy a 'fish-tank-only' meat thermometer and use it to *instantly* measure the tank water temperature. Far superior to stick on thermometers.