Wide gap semiconductors as the thermoelectric (TE) candidates have been increasingly interested because of their inherent high Seebeck coefficients and low thermal conductivities. Ga2Te3 is one of the typical defect compounds (Eg=1.65 eV) among the A2IIIB3VI type semiconductors, in which there are periodically self-assembled 2D vacancy planes that wrap the nanostructured domains. The vacancy planes scatter phonons highly effectively and are responsible for reducing the lattice thermal conductivity. Hence Ga2Te3 might be a good TE candidate. In the phase diagram of Ga-Te, Ga2Te3 is involved in the eutectoid and peritectic reactions at the critical temperatures (CTs) of 680 10 K and 757 10 K respectively. These reactions would lead to the generation of enthalpies of reactions, and induce the alteration of some thermo-physical properties. In the present work, we have not observed the phase transformations at CTs in the Ga2Te3-based materials with sulfur isoelectronic substitution for Te, which are prepared by powder metallurgy with the spark plasma sintering (SPS) technique, but can observe the generation of assumed enthalpies of reactions near CTs, which directly gives rise to the critical acoustic charge transport behaviors. The critical behaviors involve the remarkable increase of heat capacities and Seebeck coefficients and, at the same time, reductions of thermal diffusivities (thermal conductivities) and electrical conductivities. For example, the Seebeck coefficient () at x=0.05 increases rapidly from 376.3(VK-1) to 608.2(VK-1) when the temperature rises from 596 to 695 K, and then decreases to 213.8(VK-1) at 764 K. Similarly, all the S-doped samples, which have lowest electrical conductivities ( ) of 2.12102 (x=0.05), 0.25102 (x=0.1), 0.12102 -1m-1 (x=0.2) and 0.14102 -1m-1 (x=0.3) at 696725 K, undergo dramatic changes when the temperature rises to about 750 K, and then the electrical conductivities begin to decrease, and the changes tend to slow down. It is notable that both the Seebeck coefficients and electrical conductivities exhibit a typical zigzag temperature dependence in the temperature range from 596 to 812 K. These behaviors reveal the remarkable alterations in scattering mechanism of both phonons and carriers at temperatures near the CTs. Although the materials with these critical behaviors near CTs do not have satisfactory thermoelectric performance (ZTmax=0.17 at 793 K for x=0.3) as compared with the known binary Cu2Se, Ag2Se(S) or ternary based AgCrSe2 alloys, however, the findings of such critical transport behaviors have a great significance for future researches.