Tires are manufactured with a rubber compound that delivers maximum traction at a small temperature band. Some rubber compounds have wider ranges than others. We need to be there, in that temp. The starting temperature is measured after the bike has been used and the tire has been sitting in the shade for 15 to 20 minutes.
Hot temperature is as the bike was exiting the track.
Different tracks required different starting temps. Lower tire pressures also allow the tire to flex and conform to track surface irregularities for better traction. If cold rear tire pressure is too high and the tire doesn't reach best temp during your race or perhaps even never during your race - you lost the advantage of traction. Different riders with different riding styles used different cold tire temps, but we all settled on the same pressure rise as optimum - even on different tires. So, pressure rise from cold to hot was a good constant setup concept.