  We carried out a comprehensive study of the structural, electrical transport,
thermal and thermodynamic properties in ferrimagnetic Mn$_3$Si$_2$Te$_6$ single
crystals. Mn and Te $K$-edge X-ray absorption spectroscopy and synchrotron
powder X-ray diffraction were measured to provide information on the local
atomic environment and the average crystal structure. The dc and ac magnetic
susceptibility measurements indicate a second-order paramagnetic to
ferrimagnetic transition at $T_c$ $\sim$ 74 K, which is further confirmed by
the specific heat measurement. Mn$_3$Si$_2$Te$_6$ exhibits semiconducting
behavior along with a large negative magnetoresistance of -87\% at $T_c$ and
relatively high value of thermopower up to $\sim$ 10 mV/K at 5 K. Besides the
rapidly increasing resistivity $\rho(T)$ and thermopower $S(T)$ below 20 K, the
large discrepancy between activation energy for resistivity $E_\rho$ and
thermopower $E_S$ above 20 K indicates the polaronic transport mechanism.
Furthermore, the thermal conductivity $\kappa(T)$ of Mn$_3$Si$_2$Te$_6$ is
notably rather low, comparable to Cr$_2$Si$_2$Te$_6$, and is strongly
suppressed in magnetic field across $T_c$, indicating the presence of strong
spin-lattice coupling, also similar with Cr$_2$Si$_2$Te$_6$.
