From high to low lookout below
I kind of asked this question before but I've thought about it more. There is a phrase 'from high to low (temperature or pressure), lookout below'. I thought that if you fly at the same (true) altitude from a high pressure to a low that the temperature would increase, based on the fact the high has cold air and low has warm air. If that is the case, then you should lookout below when flying from right to left in the below diagram, and from left to right. I know that can't logically be true (you'd constantly be looking out below!), so where have I gone wrong?
I have a feeling it might be my statement that the temperature would decrease from low to high (10 to 5 in my example) at a given altitude.
Note, I added the green and pink to the diagram, so those are the bits that are probably wrong somewhere!