Actually you usually serve cranberry sauce at room temperature.
Cranberries are rarely served hot. When people ask this question they’re usually talking about cranberry sauce as not many people choose to eat raw cranberries.
Most of the time cranberry sauce is served at room temperature to go along with the Thanksgiving turkey.
Some people though suggest that it’s better if it’s warmed up slightly, saying that the flavor comes out a little more when it’s mildly heated.
Others like to prepare their homemade cranberry sauce the night before, and then put it in the refrigerator overnight and serve it chilled the next day.
So it’s really a matter of what you prefer but generally it’s served at room temperature.
If you were talking about other ways of eating cranberries, then serving them cold would be best.
For instance eating raw cranberries are best eaten at room temperature or slightly chilled. Raw cranberries are very sour and so just like with a lemon, it’s more satisfying to eat them cold rather than warm.
If you’re talking about drinking cranberry juice then like any other juice it’s better cold.
Some people like to eat their own homemade, cranberry compote or fruit sauce. This is kind of like homemade applesauce but with cranberries instead.
What they usually do is put some fresh cranberries, a little bit of water, and a tablespoon of sweetener or sugar in a pot and let it cook on very low heat. Then they mash it up, keep it in the fridge overnight to chill, and create their own tasty version of cranberry sauce that can be put into oatmeal, breakfast cereals or even eaten straight out of the bowl.
Hope this helps.