Everything described above is aimed at long-run, road racing sessions. In a 2-3 lap qualifying run or single lap autocross racing, the tires will not have a chance to heat up as much. Under these conditions, you will actually have to tune the handling balance using "cold" tires and therefore the cold pressures will be higher than for road racing practice or race sessions, and closer to the car manufacturer's cold tire settings (assuming similar tires).
The principles of tuning are the same, though. Make a run, make notes as to the handling performance, adjust the pressures in small increments, and repeat the test runs until the fastest lap times point to the correct pressure settings. Compensating for ambient temperature changes throughout the day also applies.
Something that we've noticed with many stock street cars is a significant differential in the front and rear tire heat potential. In theory, all four tires should be contributing as equally as possible to the overall traction of the car. In theory, they should all use close to the same pressures, and run close to the same temperatures. However, the typical stock street car, especially front-drive cars, do not follow this in practice.
In a race car, the chassis (assuming adjustability of springs, shocks, sway bar, etc.) has been set up to provide as close to neutral handling as possible for most circumstances. This is the fastest setup, and it provides equality among the four tires close to the theoretical perfect balance. However, it takes an experienced driver to know how to handle the car at the limit, or in emergency maneuvers. With many suspension adjustments to achieve neutral handling in a race car, tire pressure is used for very fine tuning of the setup.
Most street cars are not set up for neutral handling. A front drive car will typically have significant understeer. While this is not conducive to fast cornering, if someone is driving too fast around a corner, the front wheels will slide and not turn the car as much as expected. The natural reaction of the driver to this is to lift off the gas which is the right thing to do to regain some traction. In a car that oversteers, lifting off the throttle reduces traction on the rear tires and actually causes even more oversteer, and will often induce a spin. Therefore, an understeering tendency becomes a positive "safety feature" for a street car and the average driver.
Back to the theory that all four tires should contribute equally to the cornering grip. There are also two other dynamics that work the tires and generate heat: accelerating and braking. In a rear drive car, the rear wheels have the workload of acceleration and the tire heat generated. The front tires handle the majority of the braking load and the heat buildup. While the two are likely not equal, it does help to distribute the workload and keep the heat buildup shared. In a front drive car, the front tires have the workload of doing both braking and accelerating. Furthermore, a factory stock front drive car probably has a tendency towards understeering in the corners, and that adds even more heat to the front tires from the excessive cornering friction. This combination conspires to heat up the front tires a great deal more than the rear tires.
During a driving session on the track, the front tires may increase as much as 9 to 10 psig from the cold setting. The rear tires on that same car may only come up 4 to 5 psig. This clearly points out that the car is far from having the front and rear tires contribute equally to handling grip. This is not optimum at all, and requires cold pressure settings at a seemingly odd starting point.
If we look at the example situation above, we may find from testing that when the tires are hot, a reasonably neutral handling balance occurs when the front tires are at 34 psig and the rear tires are at 35 psig. If we know that the front tires are going to increase in pressure by 9 psig from a cold setting, then the appropriate cold setting is 34 minus 9, or 25 psig. The rear tire cold setting would be 35 minus 4, or 31 psig. This may sound completely counter intuitive considering that on the street, and when you first go out on the track for the first few laps, these settings will feel absolutely horrible (this setting will likely result in a lot of oversteer and will feel very loose). However, on the track, on about the third lap, the handling will settle down and should reach a neutral balance.
Remember that what matters is how the car handles in long runs, and it is the hot pressures that are to be focused on. If this means starting out with some seemingly strange cold settings, so be it.
As an aside, the best thing to cure significant understeer, and the first money that should be spent on any factory car with excessive understeer is a rear anti-roll bar. As a first modification, this will probably result in more lap time improvement per dollar spent than anything you can have done to the car.
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