What kind of heater are you using? Is it one that is preset or can you adjust the temperature that it keeps the water at? If it's a preset one, there's not much you can do about that. If you want to keep a heater in your room you can, but only if you're comfortable with it yourself - don't make yourself sweat here.
Don't put it too close to the tank, though, as it could cause it to actually overheat. Some fluctuation in temp is going to be natural, although 75-80 does seem a little drastic. Are you using an in-tank thermometer to help keep track of things?
Continue to try various methods to get him to eat. The pellets I had for my male were so tiny I was amazed but they were still too big for my girl. Remember they expand once they're in the water so by the time your betta gets his mouth around them, they may be too big to swallow.
I have heard of betta owners, especially those who breed them, keeping a small amount of aquarium
salt in their tanks at all time. A prophylactic, my betta book calls it. Dictionary . . . dictionary . . . ah, prophylactic: a preventative measure. That said, I personally don't know anyone who does this so I can't speak for long-term results. If you want to continue keeping salt in there, switch to aquarium salts, not epsom salt.
You haven't even had your little guy a week so give him some time to settle in. Sometimes adrenaline kicks in and they seem fine the first night or so but when it wears off, they have to adjust to things. I know, it's very easy to worry about them.
My male adjusted right away but he's also the carefree and kinda dense kind of guy. In contrast, my female took several days to adjust and I fussed and worried over her the entire time. I've had her roughly two weeks and she's now pretty much completely adjusted, but she still clamps up occasionally when there's a sudden movement near her tank (she hates cameras). So, it does take time. It's hard to be patient, especially when they aren't eating, but sometimes time is what they need.