This depends on where you live. If you live in a place where it is relatively in the 80's throughout the year with no temp fluctuations (even at night)then no, it's not 100% necessary, though it's still recommended. Keep in mind, that if you do live in a place like this, and have AC in your house, you will still need a heater.
If not, then yes, you should get a heater. Because bettas are tropical fish, they require a temp of 78 - 82 degrees F. If you live in an area that has temp fluctuations or gets lower than 78 degrees F during any season, then a heater is necessary. Temperatures not in this range can cause your betta to have a compromised immune system and may become prone to illnesses. He may "survive" in temps out of this range, but he will not thrive.