In the recipe for IMBC it says to let cool for about an hour in a cool place. So should I put it in the fridge?

I would say no b/c once you put it in the fridge you are going to have to let it come back to room temp to be able to spread it (the butter gets hard). My recipe doesn't say anything about letting it cool for an hour and I don't know why that would be necessary. After beating it as long as I did and adding the butter, it wasn't that warm!? Maybe someone else can provide better insight for you!

Thank you, that was exactly what I needed