This paper focuses on the electro-thermal modeling of an electrical current sensor, based on the Rogowski Coil transducer. We exploit the multi-domain capabilities of VHDL-AMS together with geometrical Finite Element Analysis (FEA) to create a time-dependent parametrical model which is able to compute concurrently the thermal and electrical variables of the system. This is particularly convenient for evaluating the temperature effect in the analogue and digital signal processing of the sensor. Some key geometrical and inner material properties of the sensor and its environment, which are difficult, or even impossible to simulate dynamically in a classical lumped-element model, are taken into account in the proposed model. This modeling technique can be used to improve the accuracy in the design of the self-calibration circuit of the sensor.