One of the challenges for single-screw micro-extrusion or additive manufacturing (AM), thus 3D printing, of polymers is controlling the melting efficiency so that energy and equipment costs can be minimized. Here, a numerical model is presented for AM process design, selecting acrylonitrile−butadiene−styrene (ABS) as viscoelastic reference polymer. It is demonstrated that AM melting is different compared to conventional melting due to variation in extrusion dimensions, leading to a different balance in heating by conduction and viscous heat dissipation as caused by the shearing between the melt layers in the associated film layer near the barrel. The thickness of this melt film layer is variable along the screw length, and it is shown that simplified models assuming an overall average value are too approximate. It is highlighted that the screw frequency, pitch angle and compression ratio are important process parameters to control the point of melt finalization. In addition, the power-law index reflecting the shear thinning nature of the polymer melt is showcased as a key parameter. Moreover, AM process results assuming constant and temperature dependent specific heat capacities and thermal conductivities are compared. The current work opens the door for on-line AM process control, addressing all relevant operating and material parameters.