The temperature sort of makes sense although not sure if the difference would be great enough to be conclusive, can't say I'm convinced on the 4psi one what is the physics behind it?
It's been around for a long time and is really quite accurate, especially on 4wd's as tyre size and construction change for different trips or surfaces, not to mention that tyre pressure changes multiple time a day as the terrain changes( i usually run 12psi on sand dunes, 18psi on rock ledges and 24 on rutted climbs) pressure changes are all about getting the right contact patch on the ground, being able to find the right pressure for your tyres mean's you will use less fuel and have less tyre wear. As the tyre carcass moves and flex's it creates heat, as the air inside the tyre heats up it expands and the pressure increase's, if the cold pressure is to low than you get to much sidewall flex and heat therefore a higher pressure increase, conversly if the starting point is to high the sidewall does not move much and less heat is generated resulting in less of a pressure buildup. The sweet spot for tyres (and also interestingly air suspension bellows) is a cold pressure that gives an increase of around 4psi, this gives you the optimum tyre pressure for your driving. Now this can be used for anything, for example if you are racing you are maintaining high speeds and cornering forces so the tyre gets hotter, once again if you play around to find your cold pressure starting point that gives you 4psi increase than you will optimise your contact patch on the road.
Give it a go, you'll be surprised just how much the pressure will change in your tyres after they have warmed up. Now a disclaimer if that 20-30 min drive includes 15min sitting in traffic than that does not count, if your sitting on the freeway at a constant high speed than you may only need 10 min's for the tyre to get up to operating temp, just bare in mind you don't have to be anal about the time thing more just a bit of common sense as to "is the tyre hot".
