Buttercream icing - do I need to put in fridge?

[babyOcho]

Am going to make some buttercream icing and stick it in the sponge cake that I baked.
Am going to ice the cake with the ready roll stuff but wont be eating it until tomorrow.

Do I need to put the whole cake in the fridge because of the buttercream??

would be ok somewhere cool instead.

iv always put mine in our poorch (winter only obviously) kids birthday cakes ect that iv made the day befor its always been fine