To understand how the thermal conductivity (TC) of virgin commercial polymers and their composites with low graphite filler amounts can be improved, the effect of material choice, annealing and moisture content is investigated, all with feasible industrial applicability in mind focusing on injection molding. Comparison of commercial HDPE, PP, PLA, ABS, PS, and PA6 based composites under conditions minimizing the effect of the skin-core layer (measurement at half the sample thickness) allows to deduce that at 20 m% of filler, both the (overall) in- and through-plane TC can be significantly improved. The most promising results are for HDPE and PA6 (through/in-plane TC near 0.7/4.3 W·mK for HDPE and 0.47/4.3 W·mK for PA6 or an increase of 50/825% and 45/1200% respectively, compared to the virgin polymer). Testing with annealed and nucleated PA6 and PLA samples shows that further increasing the crystallinity has a limited effect. A variation of the average molar mass and moisture content is also almost without impact. Intriguingly, the variation of the measuring depth allows to control the relative importance of the TC of the core and skin layer. An increased measurement depth, hence, a higher core-to-skin ratio measurement specifically indicates a clear increase in the through-plane TC (e.g., factor 2). Therefore, for basic shapes, the removal of the skin layer is recommendable to increase the TC.