Transient heat transfer problems with phase-changes, also known as the "Stefan problems" or "moving-boundary problems," are practically significant in many engineering and technological fields. Injection molding, one of the most widely used plastics processing techniques, mainly consists of filling, packing, and cooling, and the cooling stage is crucial since it considerably affects the productivity and quality of the molded parts. Thus, solutions for transient phase-change heat conduction problems during injection molding will be instructive. In this article, the enthalpy transforming scheme proposed by Cao and Faghri, which could handle the Stefan problems for generalized multidimensional phase-change structures, is applied coupled with the control-volume/finite-difference techniques. Considering the polydispersity and hierarchical structures, the polymer extended phase change temperature range or mushy zone was included in the two-dimensional enthalpy formulation to forecast the transient phase-change heat conduction during the cooling stage for injection-molded high density polyethylene (HDPE) parts. Experiments were performed and good agreement has been achieved, which reveals that the enthalpy transforming model gives good prediction, especially for the cooling analysis for the injection molding of thick-walled parts of crystalline polymers. The understanding of the phase-change heat conduction characteristics may facilitate the optimal designs of polymer injection molding process for industrial applications.