Hot air temperature inside the tire is usually below the tread surface temperature. If you only have tread temps, start with a value a little below them and refine with a gauge.

Predicted hot pressure
37.8psi
Rise
7.8psi
Temperature ratio
1.174
Absolute ref.
14.7psi

Dry air, sealed tire, ideal gas law. Moisture and carcass stretch change the real rise, so always confirm with a gauge.