This work describes a method for calculating pressure fields from temperature and velocity data in non-adiabatic compressible flows, such as the flow around a cooled turbine vane. Prior studies have demonstrated the ability to use particle image velocimetry methods to estimate the pressure gradient in the momentum equation, which is subsequently integrated to produce pressure fields. Due to changes in total temperature for non-adiabatic compressible flows, pressure fields cannot be computed from velocity measurements alone and temperature data must also be provided. In this work, a benchmarked steady 3D RANS simulation is used to generate velocity, temperature, and pressure fields in the transonic flow around a high-pressure turbine inlet guide vane. A procedure for solving the momentum equation and integrating for pressure is developed for non-adiabatic flows. Error is assessed by comparing calculated pressure to CFD predicted pressure, and the effects of PIV spatial resolution and measurement error are considered. The accuracy of the method on non-adiabatic flows is assessed using a vane with extensive film cooling. A clear benefit of incorporating temperature measurements in the pressure determination method is demonstrated, offering opportunities for deeper understanding of aerodynamic losses and entropy generation in cooled turbine flowfields.