There are so many types of sake today that should be drunk cold, that we almost end up thinking cold is the only way to drink sake. No: sake is a drink that can be enjoyed at a wide variety of temperatures, from 0 degrees Celsius ("ice sake") to 55 degrees. As such, it is probably unique in the world. Shaoxing wine from China is also delicious when warmed, but I do not know whether that can be drunk very cold. And there are some wines that can be had warm, but that are inferior types like Glühwein. The sake that is also delicious when warm, is high quality junmai sake.
What has made the image of warm sake bad, is the custom to drink cheap sake very hot. This not only happens abroad, but also in Japanese izakaya where piping hot sake ("tobikiri-kan") is served to hide the fact that it is rather tasteless stuff with lots of diluted brewing-alcohol added for volume plus sugar for taste. The result is a sort of jet fuel, of which the alcohol fumes blow in your face. Good sake should never be made really hot - just above body temperature, or lukewarm (40 degrees), is the best. In that case, it gives a very comforting feeling.
Where does the custom to drink sake warm come from? It has been recorded that when Emperor Saga (785-842) went out to hunt on a certain autumn day, the weather suddenly turned cold and the Minister of the Left, Fujiwara no Fuyutsugu (775-826), offered him warm sake. The Emperor was so delighted at this (according to the story) new way of drinking sake that he ordered that from then on in autumn and winter sake should be served warm in the palace. The idea may have come from China, where the custom to drink wine warm goes back to at least the Tang-period .
The best sake to drink warm is junmai, or a sturdy honjozo. Also Kimoto and Yamahai type sakes are delicious when warm. Perhaps not by coincidence, these are also the sakes that normally are better at room temperature than cold.