In order to elucidate the origin of the temperature ($T$) dependence of spin-dependent tunneling conductance ($G$) of magnetic tunnel junctions (MTJs), we experimentally investigated the $T$ dependence of $G$ for the parallel and antiparallel magnetization alignments, ${G}_{\mathrm{P}}$ and ${G}_{\mathrm{AP}}$, of high-quality $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnSi}$ (CMS)/MgO/CMS MTJs having systematically varied spin polarizations ($P$) at 4.2 K by varying the Mn composition $\ensuremath{\alpha}$ in $\mathrm{C}{\mathrm{o}}_{2}\mathrm{M}{\mathrm{n}}_{\ensuremath{\alpha}}\mathrm{Si}$ electrodes that exhibited giant tunneling magnetoresistance ratios. Results showed that ${G}_{\mathrm{P}}$ normalized by its value at 4.2 K exhibited a notable, nonmonotonic $T$ dependence although its variation with $T$ was significantly smaller than that of ${G}_{\mathrm{AP}}$ normalized by its value at 4.2 K, indicating that an analysis of the experimental ${G}_{\mathrm{P}}(T)$ is critical to revealing the origin of the $T$ dependence of $G$. By analyzing the experimental ${G}_{\mathrm{P}}(T)$, we clarified that both spin-flip inelastic tunneling via a thermally excited magnon and spin-conserving elastic tunneling in which $P$ decays with increasing $T$ play key roles. The experimental ${G}_{\mathrm{AP}}(T)$, including its stronger $T$ dependence for higher $P$ at 4.2 K, was also consistently explained with this model. Our findings provide a unified picture for understanding the origin of the $T$ dependence of $G$ of MTJs with a wide range of $P$, including MTJs with high $P$ close to a half-metallic value.