Maybe I’m missing context, but why the downvotes on this?

Three of the six currently operating maglevs are in communist china

I’m more of a chemist than a physicist but I had a similar difficulty understanding fractional distillation.

If the concept maps, the key thing is that the length of the path through the heat exchanger means a lot here, and that different parts of the heat exchanger can have different temperatures.

With short path lengths/little exchange time you’d have a heat exchanger like you describe - It just reaches a temp half way between the two regions it connects. But, imagine you replaced the single heat exchanger in this setup with two heat exchangers hooked up in series with a unheated middle room connecting them - Then the outside temp could be 0C, the first heat exchanger temp would be 5C, the small room’s temp would be 10C, the second heat exchanger would be 15C, and the heated room would be 20C.

In this situation, the air coming out of the second heat exchanger and into the heated room is 15C instead of 10C.

There’s no actual need for the middle room, you could directly attach the two heat exchangers end-to-end to achieve a similar result.

In essence, a heat exchanger that heats the incoming air to 18C is just a bunch of the heat exchangers that you are thinking of stacked so that the output of one is the input of the next, with a temperature gradient that forms between them.