You could put one betta in any size tank you really wanted. The problem is your tank will look extremely barer with only one fish. I personally wouldn't go bigger than 5 gallons. BTW, NEVER put 2 male bettas in the same tank.
/i19.photobucket.com/albums/b153/yesac1/Floyd.jpg*I'm a tab bit frustrated*
No, you do not need a heater, and that is not true, bettas that have heaters DO NOT live longer than ones without.
Bettas themselves get frustrated when they can't keep still, or in the same place. While a betta likes to move around, it does not like be Pushed around or having resitance.