The mayonnaise you use on your sandwich and the Hollandaise that's spooned over your eggs Benedict are the closest of culinary siblings. Each is made by slowly whisking together an egg yolk with fat, vegetable oil for mayonnaise and butter in the case of hollandaise sauce. Traditionally, mayo is used for cold foods and hollandaise or its variations for hot dishes, but it doesn't necessarily need to be that way. You can heat mayonnaise and use it as a sauce, making it a sort of faux-hollandaise without the saturated fat.
Low, Steady Heat
Mayonnaise is tricky to heat, because it contains eggs. The eggs will cook if they're heated too aggressively, so the secret is low, steady heat. Bring water to a gentle simmer -- not a boil -- in a small saucepan, and set a heatproof bowl on top with the mayonnaise in it. Whisk the mayo continuously until it's hot, then spoon it over your food. Heated mayonnaise doesn't have the buttery richness of hollandaise, which is rather the point, but its more neutral flavor gives you room for creativity. Add citrus, saffron, garlic, curry powder or other flavor accents to custom-tailor the sauce to your food.
About Food Safety
There's a persistent myth that mayonnaise puts you at high risk for food-borne illness if it's not kept cold. In truth, commercial mayonnaise is not only pasteurized, it's acidic enough to kill bacteria on contact. Homemade mayonnaise doesn't have that advantage, so it must be heated until it reaches 160 degrees Fahrenheit when tested with an instant-read thermometer. Both commercial and homemade mayonnaise should be kept at 140 F or above until they're served to prevent bacterial growth.