The thermal properties of the mold influence the cooling situation in the injection molding process. While there are experimental studies investigating the influence of special mold materials, they are limited to few polymers. In this work, an extensive parameter study with the simulation software Autodesk Moldflow Insight was performed to analyze the influence of the polymer itself on the impact of the mold steel on cycle time and warpage. The investigated part was a box with two thickness variations. A conventional mold steel was compared with a steel grade featuring approximately double the thermal conductivity. Simulations were performed with 18 polymers covering the most common material families. The main finding of this study was that the influence of the higher mold conductivity on cycle time ranged from an almost negligible reduction (3%) up to a strong effect (24%), depending mainly on the used polymers, but also on the part thickness. For the cycle time reduction, a correlation was found, with the melt, mold and ejection temperature being the dominant influencing factors of the polymers. With this correlation, it was possible to estimate the potential of cycle time reduction for other polymers. The simulations also showed a positive influence of the higher mold thermal conductivity on part warpage.