Even though an unheated 1 gallon isn't a great home for a betta, don't you think it's a lot better than those tiny cups? I mean, right now I'm keeping to bettas in there own 1 gallon critter keeper. Compared to those dirty little cups, do you think they are happier?
Absolutely. Anything is better than the cups. Remember, the cups are tiny, have no substrate or hiding holes, heater, lighting, and anything else. While you may be lacking heaters, you have given them space and things to explore. It isn't an ideal place for them to live forever, but as a temporary home it's great.
Other tan the fact that it isn't warm enough, a 1g is otherwise sufficient. Just be sure to change it every 2-3 days. Toxins build up fast in a 1g. I have also heard of people succeeding in keeping 1gs at 80 degrees with a hydor mini heater 7.5w.
You might want to look into getting 5g tanks and dividing them in 2 or 10g tanks and dividing them in 3. that way you don't have to buy a filter and heater for every betta and cleaning willl be easier.
I had Tango in a 1.5g for 6 months before I moved him into his 16g. He did fine in there. He never even had fin rot or any other disease. As long as you're religious with the water changes, he'll be good until you're ready to move him.