Single Point Incremental Forming (SPIF) is an innovative die-less low-cost forming method. Until now, there have not been viable numerical solutions regarding computational time and accuracy for the incremental forming of polymers. Unlike other numerical approaches, this novel work describes a coupled thermomechanical finite element model that simulates the SPIF of polymer sheets, where a simple elastoplastic constitutive equation rules the mechanical behavior. The resulting simulation attains a commitment between time and accuracy in the prediction of forming forces, generated and transmitted heat, as well as final part dimensions. An experimental test with default process parameters was used to determine an adequate numerical configuration (element type, mesh resolution, and material model). Finally, compared to a set of experimental tests with different thermoplastics, the proposed model, which does not consider complex rheological material models, shows a good agreement with an approximation error of less than 11% in the vertical forming force prediction.