Between 65 and 72 degrees F is ideal for goldfish because they require high oxygen levels, and cooler water holds more oxygen. However, these fish are very hardy and adaptable, and can adapt to higher temperatures without problems - provided there is plenty of oxygenation , and good water quality.
Goldfish can live in frozen lakes as long as the water right around them stays unfrozen. However you can kill them by feeding them when the water temperature is low. The fish's body temperature has dropped so low the digestive bacteria and enzymes are inhibited so any food they eat remains undigested in their gut until spring. That can do them in.
It is probably best to give them a few months of cool water in the winter so they can rest and "hibernate". Normal room temperature should be fine for them and an aquarium heater is odd and out of place in a goldfish aquarium, not that that will stop the pet shop clerks from trying to sell you a heater and telling you the fish need it.
60-70F would be ideal for them, but they are very tolerant about temperature and can survive from about 38F (under ice) up to about 85F (the tropics).
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So most people just keep them at room temperature, whatever that may be, and that suits them just fine.
Only exception would be fancy goldfish if you live in a real cold climate, then some people will use a heater, set to a low setting, and keep the tank nice and stable around 70F.
Ian
They prefer cooler water. Around 60 degrees but do fine in 70 degrees as well, too cold will kill them, i had a brand new black moor die in one night due to cold water.
The temperature is variable .... 18-20f.