Why aren't thermal analysis of propeller done?
As a propeller turns through the air at subsonic speeds, the dynamics of creating the pressure distributions in the air surrounding the propeller blade can be accurately modeled as being isothermal (no significant and persistent temperature gradients are created) and adiabatic (no significant net heat transfer from one location to another occurs within the flow field).
This means that the thermodynamic state of the air coming into the propeller disc is almost exactly the same as its state when exiting it, and for this reason there is no significant thermodynamic analysis needed to successfully account for the behavior of a propeller as long as it is subsonic.