My brain hurts... Stop it!!!
Δp = p(T + ΔT) / T - p
Δp = change in pressure
p = initial pressure
T = initial temperature
ΔT = change in temperature
All T values must be measured in Kelvin (*C + 273.15). I think the unit of p doesn't matter but I could be wrong as measurements like psi are usually a relative measurement not an absolute. Probably best to convert to Pascals.
This of course doesn't take into effect the volume of the tire changing with pressure. I'm making the (possibly faulty) assumption that the pressure change were discussing would not significantly change the tire volume. I don't know how to model that.
The hardness of the sidewall rubber changing with temperature might all have an effect on ride quality that hasn't been discussed. This more than pressure might be the cause of what you felt at San Felasco. Modelling this due to the multiple compounds in a tire wall would be a massive PITA. Easier to do an empirical test.