I’ve had some success overwintering my peppers — I keep them in my house, heated to around 65F, and I do get a little growth, but no fruit. I wouldn’t expect much success just above freezing — they really are hot weather plants, and I would be surprised if they tolerated the cold in a small container. I did lose my entire crop this winter to bugs, though, so I might just be a little traumatized (I think my mistake was drying herbs in the same room I overwintered the peppers, so when I applied the neem oil, the bugs just waited in the drying herbs until it was safe to come out).
The different varieties do have different needs. My Birds Eye’s and Thai chilies will fruit basically no matter what I do, but the hotter varieties, like my habaneros, require a little more attention to get a good crop — topping your hab was probably much more important for it’s yield than the Thai. Generally speaking, the less you water chilis and the hotter the weather, the hotter your resulting peppers will be. On average, I tend to overwater my peppers because they don’t need it as much as the tomatoes they share a raised bed with.
If you end up with too many peppers at the end of the season (this is very likely), I’d strongly recommend making hot sauce with them. You’ll likely want to cut the habaneros with something cooler to make a more approachable sauce; my favorite is peaches, but cooler peppers like Anaheims work well if you want something more savory. If you’re looking for something really flavorful, fermenting the peppers for a couple months before rendering the sauce brings an incredible tang that’s hard to find in commercial sauces.
