I think its great your getting a heater and new place for your fish today. Im not sure what fish can be housed without a heater. its not a good idea for fish to get chilled. sounds like you have a good plan in place.
How big is the smaller tank? There are some fish that like cold water - gold fish, for example. But most of them need large tanks because they're either very big (like gold fish) or they're schooling fish so they don't like to be in small groups that you could fit in a smaller tank.
Actually, whitedevil, bettas do need heaters because they are tropical fish; the water should stay at roughly 78-80 degrees. I believe goldfish are supposed to have colder tanks, though I'm not totally sure on that.
I have kept some 'feeder' fish with out a heater when I was younger, but I'm not sure is it was the smartest thing to do. I think they were called rosies?... something like that. You might also look into fish that can be kept in backyard ponds, smaller ones of course.
goldfish prefer mid 60s, but generally not above 70. they're also very tolerant of cold temps. my dad has a koi pond with some goldfish in it and they all survive just fine every winter in chicago. as long as the water doesn't freeze solid, they'll live thru some pretty harsh winters. so yeah.. i don't think goldfish need a heater but i think they do prefer larger tanks. unless you have some really tiny ones. i think goldfish generally grow to their tank size, although i've heard of some getting quite large. they're also a really long commitment, sometimes upwards of 10 years or even decades if well cared for!
gold fish cant be housed with betta's ,firstly they are cold water fish,secondly they could start nipping at the betta,thirdly they need at least a 10 gallon tank each and fourthly and most importantly they are dirty fishes,really dirty fishes ,ammonia rises extremely quickly when they are kept in anything below 10 gallons.the tank actually smells after about 4 or 5 days of having a goldfish.
so if you dont like your betta house him a goldfish.
Have anyone of you that keep them in a bowl ever take the water temp? room temperate is what it will read. I dont live in an igloo and my house rarely gets below 70 degrees. When waters get cold fish slow down, they dont die although they will act like they are dead however its involuntary if they were in warm water they would swim away fast anways, they go into a "sleep" its not hibernation their metabolisms slow down.
Fish are ALL the same, some just cant handle colder temps while others can.
If you acclimate them to it correctly they be just fine.