The chemical tropospheric dimethyl sulfide (DMS, CH3SCH3) degradation involves several steps highly dependent on the environmental conditions. So, intensive efforts have been devoted during the last years to enhance the understanding of the DMS oxidation mechanism under different conditions. The reaction of DMS with OH is considered to be the most relevant process that initiates the whole oxidation process. The experimental observations have been explained by a two-channel mechanism consisting of a H-abstraction process leading to CH3S(O)CH3 and HO2 and an addition reaction leading to the DMS·OH adduct. In the presence of O2, the DMS·OH adduct is competitively scavenged increasing the contribution of the addition channel to the overall DMS oxidation. Recent experimental measurements have determined from a global fit that the rate constant of this scavenging process is independent of pressure and temperature but this rate constant cannot be directly measured. In this article, a variational transition-state theory calculation of the low- and high-pressure rate constants for the reaction between DMS·OH and O2 has been carried out as a function of temperature. Our proposal is that the slight temperature dependence of the scavenging rate constant can only be explained if the H-abstraction bottleneck is preceded by a dynamical bottleneck corresponding to the association process between the DMS·OH adduct and the O2 molecule. The agreement between the low-pressure and high-pressure rate constants confirms the experimental observations.