Hello, converted. If you are referring to spiciness, then no. If you are referring to a la<x>yer spread on the warmed bread of a rueban, then no. If you are referring to a pot of horseradish deliberately warmed for serving with a specific dish, say beef brisket, then idk. Yourself?
You should be okay, as long as no utensil contaminated with raw meat enters the container. Dip in a clean spoon or knife. Most condiments, including ketchup and mustard, don't need refrigeration, unless they have milk products, like blue cheese or ranch dressing. The vinegar preserves most condiments for up to a year at room temp, 75° F. Peanut butter gets a pass, too, because of the high oil content. Still, these things do have a shelf life, and if you're over a year past the use by date, chuck it out and move on.