Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is a new problem which was introduced in the preceding publication by the present author. It is directly applicable to a range of practical fire autoignition scenarios (e.g. in the storages of organic matter, explosives, propellants, etc.). Effects of kinetic mechanisms, however, need be further investigated as they are expected to alter critical conditions of thermal explosion. We consider several global kinetic mechanisms: first order reaction, second order reaction, and first order autocatalysis. It is demonstrated that kinetic effects related to reactants consumption do indeed shift respective critical boundaries. Effect of kinetics on oscillatory development of thermal explosion is of particular interest. In line with conclusions of the preceding publication, it is confirmed that temperature oscillations may develop during induction phase of thermal explosion when the effect of reactants consumption is properly taken into account. Moreover, development of thermal explosion instability through the prior oscillations is an inevitable and natural scenario. This fact is confirmed by a number of examples. Besides, effects of the other relevant parameter, Zeldovich number on critical conditions are also investigated.