This isn't too hard to solve, don't worry.
1) Guppies are tropical, and all fish need a stable temperature, so a heater is really something you need. You can get 25 or 50w heaters fairly cheap at many pet stores, Wal-Mart, and aquarium stores.
2) Keeping the lights on 24/7 will stress your fish out, and, as you've seen, cause algae to bloom in the water. It's best to keep the lights on 6 to at the most 12 hours a day (if you don't have plants, a specific number of hours isn't too important, just try to be consistant with on/off times)
3) You're going to have to do water changes at least every two weeks no matter what. This is just part of keeping fish; many of us change up to 50% of the water once a week or even more often. More frequent water changes will cut down on the number of nutrients in the water and help with algae blooms as well.
To rid the tank of the green water (unicellular algae floating suspended in the water are what makes it green) you can do a water change followed by a three day blackout. No light should get to the tank - put paper/blankets around the sides of the tank, turn off the lights, and leave it dark for three days. The lack of light should kill off much of the algae.
At the end of the blackout, rinse the filter material in a bucket of water from the tank, do a water change, and start illuminating the tank for 10 hours or less per day.