The mechanics of medical endoscopes have not fundamentally changed over the last 40 years. Most endoscopes are manually operated through Bowden cables to control the head of the device, which is known to have major limitations. We propose a shape memory alloy actuated setup to enable computer-aided control. Before a complex manufacturing of porotypes is established, the design needs to be evaluated for feasibility. In this work, an efficient design approach is highlighted, where the thermal properties for an asymmetric cross-section of the endoscope is modeled with finite elements in the transient electro-thermo-mechanical domain and the results are then transferred to a network model to efficiently evaluate operation procedures. With the proposed model approach, a fast but detailed description is established which focuses on the optimization of dimensional and material parameters and models efficiently the impact of complex dynamic operating regimes.