Due to size: NO schooling fish, eg tetras, danios, white clouds. They need to be kept in schools of 6 or more, for which there is no room in your tank.
Also, a huge problem is heating a tank like that. Since even the tiniest of heaters will cook that thing, you will need to go without, which means no tropical fish, eg Bettas, frogs, etc.
You could, however, get away with dwarf shrimp, which do not mind cold water and are okay for small aquariums. Google these guys:
-Crystal Red Shrimp
-Blue Pearl Shrimp
The cherry and amano shrimp are quite hardy, but the others are a little more delicate and expensive.
Ghost shrimp are a bit larger, but again they will be fine considering the tank size and temperature. I also hear they are quite entertaining to watch.
You could also keep snails in the tank... there are many beautiful colors and they cruise around the tank at a decent speed, making them not too monotonous. As you can imagine, they are quite low maintenance.
The only fish I have come up with that will do in a small, unheated tank is the Mosquito Fish, a livebearer closely related to the guppy. The females are bigger but the males are an inch from nose to tail at most! They are also cold-water fish who enjoy climates similar to goldfish.
On the other hand, if space is an issue and you are willing to buy a bigger tank, You should consider a Hexagonal tank. They come as small as 2 gallons, but 5 gallons take up only a few inches more of space. Tetra also makes a square 3 gallon called the Water Wonders, which comes in themes such as Finding Nemo, the Little Mermaid, etc. There are tons of great small kid's tanks out there.
Remember: Even moving up to 2 gallons will increas your options tenfold, as they make heaters small enough for 2 gallons. Then you could probably go with a betta or a sparkling gourami.
Good luck :)