
Mark H. answered 08/08/19
Tutoring in Math and Science at all levels
I can offer a very general answer..
First, you have the basic gas law: PV/T = k P=pressure, V = volume, T = temperature
Simplistically, this means a change in one parameter will change at least one of the others. The easiest example: In a closed container (V is fixed), and increase in T means P has to be higher.
The inverse is that a change of pressure changes the temperature. In weather, when a "high" moves in, it normally means the temperature rises.
The other simplistic observation is that the movement of air parcels---both vertically and horizontally---is an extremely complicated process. A "high" typically means a rise in temperature, but is caused by air sinking. In turn the sinking is caused by cooling of the air. For an example, look up the "Santa Ana" condition that occurs in southern Calif. in the fall. Cold air sinks over an area called the "great basin". This in turn increases the pressure and the surface, and therefore the surface temperature gets hotter.
In addition to the basic gas law, you also have the variables of humidity and wind speed---and a few other basic laws of physics. While all the basic are well understood, we cannot accurately predict the behavior---simply because we cannot see all the data.