What is the science behind cooling ones hot food with your breath?

It’s about how heat works. Objects, and gasses, have whatever amount of heat in them. Heat gradually moves from hotter things to cooler things by contact, at different rates depending on the difference in heat between them, and the type of material.

Hot food is a lot hotter than human the human body, as you can tell when the heat flowing from it into your mouth hurts you – because of the steep difference in heat.

The air sitting next to the food gets heated up quickly, but air is light, so it can only hold so much heat. So the air right next to the food heats up quickly and then is close to the same temperature as the food, so it only slowly cools down the food.

When air moves quickly (such as when blown), the air next to the food gets replaced quickly, and all of the new air arriving is much cooler than the food, and it all moves past the food quickly, taking heat as it goes and is replaced by more cooler air.

That’s why moving air cools things down much more quickly than still air.

@Zaku nailed it.

It is the opposite effect of when you lightly breathe warm air on your cold hands to warm them up, the cold hands cool the air so your next breath replaces the cooled air with new warm air.

@Zaku‘s response hit the high points. There’s also one other effect at work here, which is Bernoulli’s Principle. This also applies to @zenvelo‘s response, but in an opposite way.

When you blow on hot food to cool it, you purse your lips and blow ‘hard’ (or as hard as you choose to, anyway) which actually cools the air that you’re blowing from your own body. (It also helps to collect more surrounding air to move with your own internally-generated volume of air and CO₂, and tends to cool that air slightly, too.) So, the harder you blow (and the bigger volume of air that you blow), the more cooling can take place, at least to some practical limits. (If you could blow hard enough to re-freeze the food, then you would probably also blow it all away in the process.)

The way this applies to @zenvelo‘s response is that when you breathe on your hands to warm them, then you don’t ‘blow’ air from pursed lips: you don’t want cooler air! So you exhale open-mouthed (mostly), which tends to keep that exhaled breath at or near your internal body temperature (warmer than your hands, anyway).

I’m sure that evaporation of water vapor (steam) from the hot food is also affected by the blowing of any air over the hot food, as removing that heated vapor-laden air (even by relatively warm air or breath) keeps the temperature differential (Δt) between the food and the ambient air as high as possible, so that evaporation can continue to occur at the fastest rate possible under those conditions. Still, for most foods, most ambient conditions and most mealtime-likely time horizons, it’s the cooler air doing most of the work.