Melt butter in a saucepan over medium heat until a pinch of flour sprinkled into the oil will just begin to bubble. Whisk in flour to form a thick paste the consistency of cake frosting. Continue cooking, whisking constantly, until flour has turned golden and begins to smell like toast, about 20 minutes. Whisk in wine, mustard, and cayenne.
Mix heavy whipping cream into the flour-butter mixture; cook and stir until thickened, about 5 minutes. Add fontina cheese; stir until melted, about 1 minute. Transfer to a fondue pot.