Hi Phil. :)
You are going to need a heater. Bettas are tropical fish and need water in the 78-82 range for optimum health. :) If your bowl is less than a gallon, I suggest upgrading ASAP to at least a gallon, more if you can. Less than a gallon is not safe to heat for you or your fish.
I would up your water changes to two 50% changes per week and one 100% change at the end of the week. For instance, a 50% change on Monday, another one Thursday and then a 100% change on Saturday. Don't use filtered water - take it straight from the tap and add dechlorinator. Filtered water doesn't have the minerals a fish needs. :)
I would definitely cut back on feeding - maybe 3 pellets twice a day, maximum. Remember that his stomach is the size of his eye, so don't overfeed. Also make sure that you remove uneaten food. Don't be worried if he isn't eating much yet - bettas sometimes take a while to settle in enough to want to eat. :)
I would also suggest covering the top of that bowl with clingwrap and poking a couple of air holes in it. Bettas can and do jump, so an open-topped bowl like that could lead to disaster.
I hope this helps. :)