There are several species of fish that can be kept at room temp, i.e. white cloud mountain minnows, some cory cats (C. paleatus), rosy barbs and so on. I kept these three species some years ago and never had any problems. Kept them at medium hardness and PH.
Since the tank is quite small, I'd perhaps try a shoal of white clouds. They're easy to breed and don't go after their young to much. The tank should be planted with i.e., Cabomba, Myriophyllum or similar plants as a breeding substrate.
Those are fish that prefer water of moderate temp, not real coldwater fish though.
To keep real coldwater fish you must assure the water never gets to warm and is well aerated. Could be a problem in summer depending on where you live.
The most interesting coldwater fish I've ever had were the good old threespined sticklebacks (freshwater form). They are very territorial and aggressive when breeding and hence should be kept without other species. The males build nests from plant parts and care for the young. In a 10 gallon I'd only keep one male with perhaps two females and provide them with enough hiding places and plants (which they may destroy when building nests).
There are also several other small species, which I have no experience with.
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Gisela
moppel@gismo.owl.de