Conjugate Heat Transfer (CHT) analysis allows for the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the solid/fluid interfaces. This exchange is especially important for MPD thruster analysis due to the high temperature plasma (∼5000K) heat transfer exchange between the plasma/Cathode and plasma/Anode electrode interfaces. Proper numerical modeling captures both the large electromagnetic current and magnetic field gradients, as well as, the heat transfer thermal gradients, that occur due to large thermal and electrical diffusion coefficient differences at the plasma/solid interface. Although MPD-CHT models are typically not included, attention to such numerical detail yields an improved MPD thruster design process and provides guidance to determine external heat transfer cooling requirements to maintain proper operating parameters. The non-linear coupled finite element formulation herein provides increased stability and presents a computational framework strategy for modeling and analysis of self-field and applied field MPD thrusters considering the highly non-linear, multi-disciplinary, and temperature dependent property requirements of the integrated solid/fluid MPD problem domain. A single numerical modeling design variable (OMEGA) is also introduced that combines experimental and numerical parameters, with reference plasma thermal properties.