How should grapes be refrigerated?

Fairly sure you can just bung them in the fridge and consume within 3 or 4 days of opening.

You can refrigerate them or just leave them out on the counter.
They won’t go bad or anything. It’s all a matter of whether or not you like them cold!

In my stomach?

The recommended storage temperature for grapes is 30–32 degrees, colder than the average home fridge (their high sugar content keeps them from freezing at this temperature). This temperature range stops or slows the fungi that commonly attack grapes.

The University of Ohio Extension Service says that for commercial storage of grapes the temperature should be between 32 and 36 degrees F (0 to 2 degrees C) and the relative humidity should be between 90 and 100%. If you add in SO2 microgenerators to the storage units and maintain a slightly higher concentration of CO2, the grapes will be able to be stored longer with no loss in quality.

However, if you are speaking of storing grapes at home, then the best thing is to store them in the home refrigerator in a sealed container or plastic bag without washing them beforehand. The preferred temperature in your refrigerator is somewhere between 35 and 38 degrees F (1.7 to 3.3 degrees C). You don’t want it to go higher than 40 degrees F or food will spoil quickly.

Whatever you do, don’t reheat them afterwards using the microwave