Cupcakes with cream cheese or whipped topping are best stored in the refrigerator in an airtight container or wrap the box in plastic wrap up to 48 hours. All buttercream topped cupcakes can be stored at room temperature in an airtight container or wrap the box with plastic wrap up to 48 hours Cheesecake cupcakes are best stored in the refrigerator until consumption for up to 72 hours.