no no no! people, if you aren't sure or haven't done any research on the topic please don't give crappy advice.
The fact is few fish live the wild in such confined enclosures, and by few, I mean different species of wild betta's, shrimp, and a bunch of crap that's not found very often in the trade. Even keeping shrimp can be dicey as ANY change in chemistry will kill them. Bettas are so often kept in small tanks because they can breath O2 through their labyrinth organ, meaning that bad water quality does not NECESSARILY mean death. Same principle that can be applied to gold fish in bowls. Just because the colder water means higher O2 saturation (they can breathe easier in foul water), does not mean they should be.
Take into account that your H20 changes will include a huge difference in TDS, pH, and hardness (not def on the last two, but yes on the first).
If you live in the boondocks, where you can't get much... and don't want a betta. Then my advice is to chuck it. They're cheap, and a 5-10g will fit on a desk. Don't let vanity punish animals.