The ITER Electron Cyclotron Resonance Heating and Current Drive (ECRH&CD) system relies on 1 MW 170 GHz Gyrotrons to provide the mm-wave power needed for plasma heating, current drive, and magneto-hydrodynamic control. The design and modeling of the control system of the Magnetron Injection Gun (MIG) is crucial to keep the emitter in the proper operating conditions. Within the MIG control system framework, a thermal lumped model has therefore been developed. As the MIG is characterized by a complex geometry and no temperature measurements of the system are available, parameters need to be introduced within the model, which must be optimized. This work presents a rigorous sensitivity analysis (SA) of the parameters of the MIG, intending to quantify the parameter effect on the model output to develop an ad hoc optimization algorithm. Both local and global SA will be discussed, with the latter specifically aiming at evaluating the inference between parameters. The subsequent optimization, which was carried out following the hierarchy of the parameters defined by the SA, will allow finding the optimal set of parameters for the lumped model of the MIG, which will then be validated against experimental data taken from outside those used for the analysis, proving the good results of the procedure and the determined parameter set.