One way to look at temperature is that it is the kinetic energy of a molecule. Basically, how fast the molecule is moving. When you measure temperature with a thermometer you are actually measuring the average kinetic energy impacting the device. Some molecules will be moving fast some are moving slow.
Bubbles of hot air rise in a house because the fast moving molecules push each other farther apart making the bubble of hot air is less dense (it weighs less so it floats).
When you go up a mountain there is less air.
The molecules can be moving much faster than the hot air molecules in the house (and thus be hotter), but there is less of them. So the average kinetic energy transferred to the thermometer is lower and it will show a colder temperature.
Saying hot air sinks to the valleys is pure nonsense.