He's definitely too hot.. how did you acclimate him to that water? Did you just plot the heater in and turn it on? That would have been very hard on him, and would definietly account for his behavior.
2 gallons is really minimum to keep bettas healthy long term, and then you can buy a good 25w adjustable heater. As you've learned, it's really hard to keep anything less evenly heated. Those small unadjustable heaters that are supposed to automatically turn off at a certain temp tend to fail, over heat, and/or cause lots of swings. 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. It's also important to always use heaters along with an in tank thermometer like these: http://www.amazon.com/Hagen-11200-Ma.../dp/B0002AQITA
The half gallon would also have required alternating 50% and 100% daily water changes or by the end of the week you would have seen very high ammonia.
At this point is he in the 1.5g yet? I would get a 2.5g+ with a good adjustable heater, but if you can't afford that I would get the 1.5g set up at a stable temp between 78-80 degrees and acclimate him slowly to fresh new appropriately adjusted water. After that along with good water changes of 3x weekly 50% 50% 100% or at minimum 2 at 50% 100%, he should perk up.
This is how you can do those large water changes without shocking him:
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.