This work aims at developing a training simulator for interventional radiology and thermo-ablation of cardiac arrhythmias. To achieve this, a real-time model of the cardiac electrophysiology is needed, which is very challenging due to the stiff equations involved. In this paper, we detail our contributions in order to obtain efficient cardiac electrophysiology simulations. First, an adaptive parametrisation of the Mitchell-Schaeffer model as well as numerical optimizations are proposed. An accurate computation of both conduction velocity and action potential is ensured, even with relatively coarse meshes. Second, a GPU implementation of the electrophysiology was realised in order to decrease the computation time. We evaluate our results by comparison with an accurate reference simulation using model parameters, personalized on patient data. We demonstrate that a fast simulation (close to real-time) can be obtained while keeping a precise description of the phenomena.