Unless your kitchen is very warm &/or humid, your cakes should be fine unless the directions instruct you 'fridge them.
Some folks like the firmness that a cold cake has and some prefer the warmness of a room temp one. Sometimes storing in the 'frige will dry a cake out and cause it to taste stale sooner. It's really just your choice which you desire.
I have a couple recipes that I have to store in the 'fridge and the rest sit on the counter for 2 days. Then any that is left is sliced (iced and all) and stored in the deep freeze. We loooooove to pull out a slice or two a few weeks down the road w/out having to bake a whole 'nother cake.
"I can read and write if that's what you mean. I'm not thick or anything just don't ask me where the commas go."
Incendiary by Chris Cleave