At the end of this past summer I did some testing on the calibration course on the road in front of my house with 3 different tires in different conditions. I measured the change in the calibration constant from the morning, when temperatures are lower, to the afternoon, when temperatures are higher, with different tires and with different initial conditions of the tires. The purpose was to determine the tire and the initial conditions that give the smallest change due to change in temperature, and also determine what really matters when you are trying to get the smallest change in cal constant from morning to afternoon.
You can see a description of my test procedure and the results at the link below.
I will probably continue this testing next summer. Specifically, I'm interested in testing a mountain bike type tire with knobby thick tread, just to see how bad things can get for changing cal constant. Or maybe not. That's one reason why it's good to do testing, to make sure the things we think we know are actually true.
I'd also like to test solid tires, but I don't have any to test. If someone else would like to do those tests, that would be great.