Based on full quantum transport simulations, we report a comprehensive study of the evaporative cooling process in double-barrier semiconductor heterostructure thermionic refrigerator. Our model, which self-consistently solves the non-equilibrium Green's function framework and the heat equation, is capable to calculate the electron temperature and electrochemical potential inside the device. By investigating the dependence of those thermodynamic parameters as a function of the barrier thickness and height, we answer open questions on evaporative cooling in solid state systems, and give a clear recipe to reach high electron refrigeration. In particular, simulation results demonstrate that the best cooling is obtained when i) the device operates at the maximum resonant condition; ii) the quantum well state is symmetrically coupled with the contacts. The present results then shed light on physical properties of evaporative cooling in semiconductor heterostructures and will allow to speed up the development of thermionic cooling devices towards unprecedented performances.

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