sub zero,
My 2 cents:
1) Get a heater. You're not so much using it to heat the water as to stabilize the temperature. Fish (in just about all things) like stability. The heater will only cost you a few bucks, you don't need to do much w/ it (at least not much in a ten gallon tank) and it'll make your fish happier and healthier.
2) About once a month is right. Many, many, many new fish enthusiasts decide they want to be good owners and keep a sparkling clean tank. More cleaning = better aquarium, or so they believe. Nothing could be farther from the truth. The bacteria and such that collects in your tank is 1) good for the fish's environment substantively and 2) good for promoting stability (that word again) in the tank environment. The bacteria are an important filtration device.
When you clean you want to a) scrape the sides of the tank (so you can see the fish) and then b), do a PARTIAL water change. (1/3 to 1/2 of the water at most.) The best way I've found to do the water change and get some gunk out is w/ a vacuum attached to the sink. (Python is a big brand.) If you have a gravel/sponge combo filter replace only one of the two at a time (gravel this time, sponge next time).
If'n you're bothered by a little algae that creeps up between cleanings, buy a little scraper magnet. I leave mine hung on the side of the tank for touchups. (Assuming of course, this tank is glass - don't use on acrylic.)
That's it!
Oh, Feed your fish less than you think you should feed them. (Most newbies feed their fish WAAAY too much food at a time.)
PS - The 55 gallon tank behind my head here in the office needs a cleaning if you are dying to do such work more than once a month.