If you take a good mod or good original ISI content, you'll be able to see that the lower the initial pressure you start the race with, more laps you'll need to obtain tire pressure stabilisation. So if you struggle on cold tires to follow your opponents, it may be due to too low initial pressure of tires. Inner temps (not surface) are, as is to be expected, lower on more inflated tires after a 20 mn stint. So beware of general recomendations like the lower pressure of tires is the best. Cheers.