The influences of ambient temperature oscillations on the convection characteristics generated by an exothermic reaction in a closed vessel have been investigated. The left, right and top walls of the vessel are maintained at a constant temperature while the temperature of the bottom wall is assumed to be oscillating about a constant mean temperature. The governing equations are solved using finite difference method. A demarcation line between the explosion and the oscillatory convection is presented in terms of the Rayleigh and Frank-Kamenetskii numbers. It reveals that when the heat generation is large the convection of heat to the side walls must be higher to circumvent the thermal explosion. When the frequency of oscillation and the amplitude of oscillation of the ambient temperature are increased, the intensity of the stream function and the temperature is found to increase in a certain period of time. After that, the reverse characteristics are seen in the next period of time and these occur periodically. For a certain period of time, a cooler region is recognized near the bottom wall. Results also show that for higher values of the Frank-Kamenetskii number the oscillatory convection tends to chaotic and when it exceeds a certain value there occurs thermal explosion. Moreover, the system encounters a rapid explosion with the increase of Frank-Kamenetskii number and Rayleigh number.