How do I store Buttercream Frosting?

I’m planning on making a birthday cake tomorrow which I will be bringing to school on Thursday. I plan on covering the cake with buttercream frosting. Last time I made buttercream frosting, I put the cupcake with the frosting in the fridge and it was solid. I was wondering if I apply the buttercream on my cake, if I should just leave it out over night

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