Oh no! Thats too bad it had a crack....but at least you were able to discover it before filling it up and having it leave everywhere.
And the 1 gallon will be perfect for Temporary housing until you get him something bigger so long as you keep up with the water changes and all that :)
I its quite common in the summer time if you live in a warm place(though that light might also be contributing....maybe best to just keep it off. Don't worry, he doesn't need it.)for tanks to stay on the warmer-side even without a heater...the frozen water bottle is the most commonly-used method I know of, but iced dechlorinated water sounds like it would work just as well. Just keep trying, it'll eventually cool down.
You'll want to get a heater though any way for the colder months, which are soon approaching(depending on where you live). If don't plan on upgrading before then, You could try a 25 watt submersible, adjustable(this being very important)heater. It may be a little large, but so long as its adjustable it just might work.
Perhaps check around online as well for something smaller?
Glofish are sadly not compatible with bettas, I'm don't think....they are a genetically altered version of he Zebra Danio, which are very fast-swimming, fin-nipping, schooling fish. Not only do they need to be in groups, which would require at least a 10 gallon, but their quick movement would bother a slower-moving betta, and they would likely nibble on his long flowing fins....not to mention the bright colors of the Glo-variety might spur a betta into attack-mode and he might go after them.
Glofish are sadly quite expensive for what they are and tend to be on the unhealthy side IME, as they are altered genetically with Jellyfish DNA. As pretty as they are, I wouldn't recommend keeping them with or without a betta.
But, anyway, I'm very glad to hear that Jake is doing well, and happy to see some pictures! Hes quite a lovely boy :)
Edit: Aaaaand I was beat to it :P I need to be faster...
I'd still disagree the the Glofish compatibility...but thats just my personal opinion and experience. :/