Medium and High frequency transformers (MFT/MFT) are crucial part in the design of Solid State Transformers. At high voltage and power ratings, the thermal behaviour (generated from the core and winding losses) coupled within a fluid environment (such as air) becomes very important to be investigated and analyzed. Existing studies in literature use analytical equations which often introduces errors in computation and fails to capture the dynamic interaction between the various coupled physics behaviours of the MFTs. This paper presents a combined Finite Element Analysis-based (FEA) time-harmonic electronic, thermal and fluid models for solving a shell-type MFT. A parametric optimization method is proposed to achieve a minimum MFT efficiency of 98% within the required thermal and electromagnetic constraints. The appropriate boundaries were defined for each physics with natural and forced air convention defined for the fluid model. The steady state results of the combined physics and parametric optimization show the interaction between each of the coupled physics. The optimization results shows the effectiveness of the proposed optimization and parametric values that achieves the desired minimum efficiency and maximum temperature distribution. The proposed method presents an effective way of choosing the necessary cooling methods and insulation when designing MFTs for high power and voltage SST applications.