Solid state transformers (SSTs) are at the forefront of emerging technologies, enhancing distribution and transmission networks. These transformers facilitate the development of highly controllable and robust smart grids, seamlessly integrating renewable energy sources and accommodating connections for both alternating current and direct current components/lines at medium or low voltage levels. This research paper introduces an innovative SST incorporating the inductive power transfer (IPT) technology, currently under development within SSTAR, a Horizon Europe project. This novel device operates at a frequency of 50 kHz and provides with an output power of 50 kW. The IPT system is submerged in an ester-based, biodegradable dielectric fluid, providing effective cooling and insulation characteristics. The primary focus of this research is to highlight the guidelines for the optimal design of the forced liquid cooling system of the SST module. The analysis employs a multi-faceted simulation strategy to calculate the cooling aspects of the transformer, utilizing the commercial software ANSYS. This involves 3D coupled Electromagnetic (EMAG) - Computational Fluid Dynamics (CFD) simulations, as well as stand-alone CFD and thermal FEA simulations, ensuring robust cross-verification of the obtained results. This novel SST exhibits improved thermal performance, achieving a hot-spot temperature of 58 °C, the lowest value found in similar research studies. The findings underscore the efficiency and robustness of the proposed design, marking a significant step towards the realization of active and environmentally-friendly electrical networks.