  We report the evolution of thermal transport properties of iron-based
superconductor K$_x$Fe$_{2-y}$Se$_2$ with sulfur substitution at Se sites.
Sulfur doping suppresses the superconducting $T_c$ as well as the Seebeck
coefficient. The Seebeck coefficient of all crystals in the low temperature
range can be described very well by diffusive thermoelectric response model.
The zero-temperature extrapolated value of Seebeck coefficient divided by
temperature $S/T$ gradually decreases from $-0.48 \mu V/K^2$ to a very small
value $\sim$ 0.03 $\mu$V/K$^2$ where $T_c$ is completely suppressed. The normal
state electron Sommerfeld term ($\gamma_n$) of specific heat also decreases
with the increase of sulfur content. The dcrease of $S/T$ and $\gamma_n$
reflects a suppression of the density of states at the Fermi energy, or a
change in the Fermi surface that would induce the suppression of correlation
strength.
