Would this recipe require refrigeration? If so, does anyone have a recipe that DOESN'T? Thanks for any help you can offer.

Banana Filling

3/4 cup confectioners' sugar
1/4 cup flour
1/2 cup milk
5 tablespoons butter
2 ripe but firm bananas, sliced
1 teaspoon vanilla extract
Combine confectioners' sugar, flour, and milk in a saucepan; cook, stirring, until smooth. Continue cooking until mixture thickens; transfer to mixing bowl, cover, and chill thoroughly. Beat butter into the chilled mixture, a tablespoon at a time. Fold in sliced bananas and vanilla.

Nope!