How did you acclimate him to his new water? What conditioner are you using?
Your boy is going to need a heater to keep him healthy long term.. Unless you keep your house a constant temp 80F+ (meaning not even temp swing/drops at night).
1 gallon bowls can be hard to heat though, and really 2 gallons is minimum for keeping bettas healthy long term..
You will have to use one of those preset non adjustable small ones, and you absolutely must use an in tank thermometer (something that looks like this http://www.amazon.com/Marina-Floatin...a+thermometers
) to monitor temps because they are really unreliable, tend to fail, not keep temps constant and/or overheat the water. You should also give them a test run for 24 hours in a same sized container without your fish to make sure they will hold temp and work properly. Once you have figured out they will you need to acclimate your boy slowly to the warmer water. Since these are non adjustable and you have no control about how fast the water heats up you'll have to cup him (in like a fresh plastic solo cup) and float him in the warmer water for about an hr to acclimate.
For that small 1 gallon you will need ideally 3 water changes a week 50%, 50% and finally 100% which will include a thorough rinsing of the gravel and all ornaments to remove all the poop and debris that has accumulated over the course of the week. At minimum you need 2 - one 50% and one 100% at week's end.
I also suggest using Prime as your conditioner (what are you using now?) because it will help render some of that ammonia that he will see over the course of the week harmless to him.
I would suggest not using flakes in a container that small, because you can't help but keep some of it from falling to the bottom if not just plain dissolving in the water. Flakes muck of water way faster than pellets which can be fully consumed or taken out of the water, and your 1 gallon will grow ammonia fast enough without any help. I suggest New Life Spectrum Betta pellets (feed 5-8 split up into 2 or even 3 smaller meals with one fast day a week) or Omega One Betta Buffet pellets (feed 3-4 split up with one fast day a week).
This is how to do all those large water changes without shocking your fish:
To do a water change, use a little cup like a plastic solo cup - this cup must be only for him and have never been used with soap or other chems. Scoop him up in this cup (keep him in the cup about 1/4 full of water - it doesn't need to be much because he won't be in it for long) and leave him in the cup while you change his water. To do the 50% use a turkey baster - dedicated only to him that has never seen soap or chems - and drag it through the gravel and try to suck as much of the poop out as possible, in addition to 50% of the water. Use a thermometer under the running tap to get it to be the same temp as the water that is normally in his tank. When the thermometer says the flowing tap is the right temp, fill back up his tank. At this point, add the conditioner (dose for how much water you change - if you change half the water you add half gallon worth of conditioner, If you do a 100% water change dose for the full gallon change). Float his plastic cup with him in it in the new water. Slowly add a couple tablespoons of the new water into his cup every 10 minutes for at least an hour. Finally, dump him in gently but try to get as little of the old cup water back into the tank as possible. When you do the weekly 100% you will do mostly the same thing except empty his tank fully and rinse everything in it very well under warm water but never use soaps or chemicals. Once it's fully cleaned/rinsed you can refill it and repeat the cup/acclimate phase.