Bettas don't need a heater, but the algae eater does. I really don't think you need an algae eater in that small of a tank... so you may want to consider donating the fish and saving yourself money on a heater. I've owned many bettas through the years with a couple living over 4 yrs. so you're okay.

Get a snail. Certain ones don't reproduce quickly.
We got a trapdoor snail for my daughter's 5 gallon betta tank because "Wanda" needed a maid. Snail does a great job.

http://aqualandpetsplus.com/Bug,%20Snails,%20Trapdoor.htm