It's better to let it come to room temperature before putting it in the fridge.
Although most people don't refrigerate their cakes, because it tends to dry them out. When it comes to room temperature you can wrap it in plastic wrap, and it will stay good at room temperature for several days. Or you can wrap it in another layer of foil and put it in the freezer for anywhere from 1 day - 2 months.
I let my cakes come to room temp and then wrap them in Press And Seal and then freeze them overnight (altho up to a week seems to be ok). Leaving a cake uncovered (either not wrapped up or at least crumbcoated) will lead to it drying out.
also, putting hot or even warm food into your fridge will raise the temp by a few degrees (or more if its proper hot) which could mean ur fridge becomes a whole lot more bacteria friendly.
xx
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