The possibility of tailoring key surface properties through the injection molding process makes it intriguing from the perspective of sustainability enhancement. The surface properties depend on the replication accuracy of micro and nanostructures on moldings; such an accuracy is enhanced with cavity temperature. The simulation of the injection molding process is very challenging in the presence of micro and nanostructures on the cavity surface; this does not allow for the neglect of phenomena generally considered not to influence the overall process. In this paper, a multiscale approach was proposed: in the first step, the simulation of the overall process was conducted without considering the presence of the microstructure; in the second step the outputs of the first step were used as an input to simulate the replication of the microfeature. To this purpose, a lubrication approximation was adopted, and the contribution of the trapped air, which slows down the polymer advancement, was accounted for. A modification of the viscosity equation was also proposed to describe the rheological behavior of isotactic polypropylene at very low temperatures. Concerning the microcavity filling simulation, the modification of the viscosity description at low temperatures consistently describes the process, in terms of polymer solidification. Concerning the replication accuracy, it increases with the cavity surface temperature, consistently with the experimental observations.