Tx power vs Error Vector Magnitude
You need to get the transfer function for AM/AM and AM/PM conversion for your PA to get the mathematical relationship describing the gain and phase shift for the PA as a function of input amplitude (of the envelope of the signal specifically). This describes the non-linear behavior of the PA as you increase output power toward saturation; for low power levels the PA will be linear such that an X increase (in dB) or input power will correspond to a X increase in output power, or in phase there will be no additional phase shift that is dependent on the input power level. However at increased power levels the output power change will be less than the input (AM/AM) and additional phase shift is introduced (AM/PM).

From that it should be very clear how the error vector magnitude can be modified from such a non-linearity, especially with waveforms that are not constant envelope (implying that the input amplitude is changing and this creating the AM/AM and AM/PM distortions).

Thermal heating can be a factor, such that the static AM/AM and AM/PM translations will only approximate the true effects due to the associated memory effects.  My peripheral understanding is that more advanced modeling with Markov processes can be done to more accurately predict the behavior in these cases, particularly with modeling spectral regrowth.