Some ideas for you maybe....
You could offer to wash your parents cars for 10 dollars to get a heater for the 1.5 gallon tank.
You could also get a large vase at a thrift store or other retail shop..(1.5-2.5 gallon vase) clean it real well and get a heater and some nice decorations.
You might be able to do the vase idea for around the same price as the 1.5 gallon tank,but be able to get the heater as well.
My fish Cleo lived in a 2 gallon cookie jar with a heater and live plants for 8 months.
(he's in a 5 gallon tank now though)
It was like this:
I left the lid off of course though, so he could breath and I added some nice gravel and 2 small amazon swords and he was very happy in there for 8 months.
I wouldn't get a betta if you can't get a heater though, It is very important to have a heater, because they are tropical fish.