An electro-thermal model of a Rogowski Coil sensor system is here described. A co-design methodology between VHDL-AMS and Finite Element Analysis (FEA) has been used for modeling the entire system. The proposed modeling strategy uses geometrical FEA to complete a time-dependent parametrical heat transfer model, which can be implemented in VHDL-AMS or in any other similar hardware description language. This is especially useful for performing simulations with the embedded signal processing electronics of the sensor. Important geometrical, environmental and inner material properties of the Rogowski Coil sensor system, which are difficult, or even impossible to simulate dynamically in a classical lumped-element model, are taken into account indirectly in the proposed model. This allows to study the cross-domain effects in the complete system.