It can’t be friction, because putting air into a car tire doesn’t heat it up. The answer is that when air (or any gas) is compressed, when it is forced into a smaller space, it gets hot.
When you use your hand pump, you’re compressing the air in the pump, but when you use the gas station’s air, you’re using air that has already been compressed.
The gas station’s air did indeed get hot when it was originally compressed into the storage tank. But by the time you show up with your sad-looking tires, the air has had lots of time to cool off. All you are doing is bleeding off some of that stored-up air No compression is going on, so there is no heat.
Why does compressing a gas make it hot?
Well, gas molecules are free spirits; they are flying around freely, as far apart from one another as they can get, within their confines.
To force them closer together, to compress them into the confines of a tire, for example, you have to oppose their outward-flying proclivities with some inward-pushing force. When you use your pump, the sweat on your brow tells you that you are indeed putting some of your own muscular energy into that gas.
But what do the molecules do with that energy? Unable to fly so far afield anymore, they use the energy you’ve given them to fly faster. And faster-moving molecules are hotter molecules; heat is nothing but fast-moving particles.
Thus, your muscular energy goes into heating up the gas in the tire.