We found a thermally assisted increase in anharmonic coupling between the reaction coordinate and CH(D) stretch mode for the dissociation of a single dimethyl disulfide molecule on Cu(111) induced by inelastic tunneling electrons from a tip of scanning tunneling microscope (STM). The reaction order, i.e. the number of electrons required for a reaction, changes from two to one at elevated temperature while the CH(D) stretch mode is excited by tunneling electrons. The detailed reaction mechanism is studied through the quantitative analysis of the non-integer reaction order observed at intermediate temperature, where low energy vibrational mode originated from the hybridized state of molecule and substrate plays a key role.