We all know hot air rises, right? So a mountain top would be much warmer than the valley below...right?
Hot air rises, true, but that's not the whole story, because rising air also cools. The initially hot air cools more and more as it rises, eventually getting cold.
The hot air in the valley got hot in the first place because it was warmed by the ground. The ground is much better than the air at absorbing sunlight, so the sun warms the ground, which warms the air around it.
The hot air does rise, but it gives up its heat as it rises. That's because there's less air pressure at higher altitudes, and lower pressure makes that rising bubble of hot air expand. The more your air expands, due to low air pressure, the colder it gets. That's one of your basic laws of physics.
It's warm in the valley because the air pressure is higher, and there's all that warm ground to heat the air. Up in the mountain there is lots of low-pressure air, but not a lot of ground!
