In doing a bit of research, the smallest heater I'm seeing is 7.5 watts, which is rated for a 2-5 gallon tank. On Amazon.com, someone has the hydor mini and said they used it in a 1 gal. bowl, but their house temp. was kept at 60 degrees in the winter. I bought a 7.5 W heater from Wal Mart just last week for my 5 gal. It's called Small Aquarium Heater by Junior Heater, for 2-5 gallon aquariums.
You might want to consider spending $10 and buying a 2 gal. bowl. (or larger, if you can afford it, my betta loves his 5 gal. tank.)
Definitely buy a thermometer, one that goes inside or floats in the water (Walmart, $1.98) and not the one that sticks on the outside so you can monitor the temperature. Too hot is as bad as too cold.
Good luck! Keep us posted.