The kinetics and the mechanism of the reaction of S(3P) with O2 have been studied at low (293 K) and high (980-1610 K) temperatures. The strong non-Arrhenius behavior of the overall rate constant, which has been inferred from previous measurements, was confirmed. Possible causes of this non-Arrhenius behavior were investigated. No difference was found in the product channel between high and low temperatures, i.e., the products of the reaction were confirmed to be O(3P)+SO at both low (293 K) and high (1566 K) temperatures by quantitative measurements of O(3P) atoms. No pressure dependence was found either in the rate constant or in the product yield in the pressure range 2-50 Torr (Ar buffer) at 293 K. At low temperature, the time profile of each triplet component of S(3PJ) was measured separately. The intratriplet relaxations by collision with O2 were found to be about one order of magnitude faster than the reaction with O2. An analysis of the intratriplet relaxation by O2 strongly suggests the contribution of bound multiplet surfaces, which probably have substantial barriers toward products, O(3P)+SO. These (and/or other) multiplet surfaces probably contribute the steep rise of rate constant at higher temperatures.