I wonder.
Mayonnaise is actually one of the safer food items. It has a fairly high acid and salt content, both of which are good antibacterials.
That assumes you are using commercially produced mayo and not the homemade kind, which can be a nice bacterial growth media.
Additionally, the low water activity (about .925 for Burger King Mayo), discourages bacterial growth.
I take it that Fanny’s original question applies not to spoliage of products containing mayo, but rather to the fact that (home-made) mayo contains eggs but is not cooked during preparation. Otherwise she probably would have asked in reference to refrigeration rather than heating.
And I think the answer, then, is that it uncooked mayo runs the same risk as other dishes that contain raw eggs. There is some risk of salmonella, and I definitely wouldn’t have anyone eat it that is pregnant, elderly, in a weakened physical state, etc.
Commercial mayo is also made from pasteurized eggs and the acidity actually kills a lot of bacteria that comes in contact with is. All you ever wanted to know about mayonnaise safety.
Even so, the chances of getting samonella from using raw eggs in homemade mayonnaise is pretty slim. (Something like 1 in 63,000 eggs in the US contain traces of samonella, IIRC).
As Squink said, it’s a water activity thing. Because it’s an emulsion, all of the water in mayo is tied up and unavailable for bacterial growth. So, even if Salmonella is present, it’s unable to grow to dangerous levels. The problem with mayo arises when it’s mixed with something else, say, potatoes to make potato salad. Suddenly, you’ve mixed a potential source of the bacteria (since mayo is made from eggs) with food that’s perfect for bacteria to eat. If you then mishandle it, letting it get to a temperature where bacteria can grow and letting it sit there for a while, the bacteria can grow enough to make you sick.
BTW, I should have mentioned that my degree is in microbiology.