Do batteries such as AA c and d last longer if stored in the fridge?

Storing in a fridge don't make them last longer in use, but it does make them lose less during storage.

It's like taking two glasses of water, filling them up equally, then setting a saucer like a lid on one of them and leaving the other one open.

The water level in the one left open will drop faster, just like the battery left in room temperature will lose energy faster than the one in the fridge.