How do I represent altitudinal climate variation in my map?

I'm making a Köppen Climate Classification map of my world, and I've got quite a few mountain ranges exceeding 1000 metres, which I know is going to affect the climate of the mountain. Issue is, I'm not sure *how* exactly climate changes with altitude, even after poking around here and reading about the average temperatures of each Köppen zone. Can anyone give me a hand?

I remember finding a really handy rule of thumb ages ago: essentially that for every thousand or so metres you elevate, the climate of that area will shift to that of an area a certain number of degrees poleward. I'm not sure if that's accurate or where I heard it from, but I'd *love* something like that!