Generally, genoise cake does not need to be refrigerated if it will be consumed within a day or two of baking. However, if you live in a hot and humid climate or if your kitchen tends to be warm, it may be safer to refrigerate the genoise cake to prevent any potential spoilage or bacterial growth. Additionally, if your genoise cake has perishable fillings or toppings such as fresh cream or fruit that require refrigeration, then it should definitely be stored in the refrigerator.