High-order temporal soliton compression in dispersion-engineered silicon photonic crystal waveguides will play an important role in future integrated photonic circuits compatible with complementary metal–oxide–semiconductors. Here, we report the physical mechanisms of high-order temporal soliton compression affected by third-order dispersion (TOD) combined with free carrier dispersion (FCD) in a dispersion engineered silicon photonic crystal waveguide with wideband low anomalous dispersion. Through numerical temporal soliton evolution analysis, we report what we believe is the first demonstration of the dual opposite effects of TOD on temporal soliton compression, which are strengthening or weakening through two different physical mechanisms, not only depending on the sign of TOD but also the relative magnitude of TOD-induced equivalent group velocity dispersion (GVD) ${\beta }_{2,\text{equ}}$ to the original GVD ${\beta }_2$. We further find that FCD counteracts the effects of negative TOD on the soliton compression, while it reinforces the effects of positive TOD on the soliton compression. These results will help to design suitable dispersion-engineered silicon waveguides for superior on-chip temporal pulse compression in optical communications and processing application fields.