Heat transfer simulations of the fused filament fabrication process are an important tool to predict bonding, residual stresses and strength of 3D printed parts. But in order to capture the significant thermal gradients that occur in the FFF printing process, a fine mesh discretization and short time steps are required, leading to extensive computational efforts. In this work a simulation framework is presented which combines several efficiency measures with the objective of reducing the computational efforts required in simulating the FFF printing process without simplifying the deposition physics or reducing the overall accuracy. Thus, the material deposition has been modeled with a hybrid element activation approach and elements are adaptively coarsened through an error-based coarsening condition. Additionally, an appropriate coarsening technique is presented for geometries with air-filled infill patterns. The accuracy of the numerical framework is experimentally validated and the efficiency of the framework is validated numerically by comparing the performance of models with and without any efficiency measures. Finally, its effectiveness is shown by simulating the printing process of a larger geometry.