Just looked at a write-up from Mike Sandford about change of cal constant due to temperature changes. He calls this cal constant sensitivity to temperature the "temperature coefficient," and he makes a couples conclusions about it:
1) Initial pressure in a tire doesn't affect its temperature coefficient. A tire starting its measurement day at 70% of its rated pressure will show the same change between its pre-cal constant (cooler) and post-cal constant (warmer) as it would have if it was pumped to 100% of its rated pressure at the beginning of the day.
2) Narrower tires have a smaller temperature coefficient than wider tires. Or in other words, narrower tires will have a smaller difference between pre and post cals than wider tires.