We present a modified Newton scheme applied to a thermomechanical shape memory alloy model, which improves the convergence. Key feature of the model, which is a modified version of the model by Sedlák et al. 2012, is its capability to accurately model the shape memory effect, as well as the superelastic behavior by a thermomechanical potential, compare with Sielenkämper & Wulfinghoff 2022. The variation of this potential yields the energy balance, the linear momentum balance and the evolution equations of the internal variables. Yield and transformation criteria are derived form the corresponding dual dissipation potential. In order to improve the convergence of the thermomechanical model the Newton scheme is adapted using a line search approach. Therefore, the residuum of the convex thermomechanical potential is linearized. The step size of each Newton step is adapted such that the local minimum of each step is approximated as starting point for the following Newton step. This approach improves the numerical robustness of the Newton scheme.