In this study, we investigated the limits of safe operation for a cooled reactor, operated batchwise. As an example of a single-phase reaction, we studied the decomposition of t-butyl peroxypivalate, a well-known organic peroxide, undergoing self-heating at relatively low temperatures. If sufficiently diluted, it can be supplied to a polymerization process from large, cooled but unstirred vessels. We present a number of extensions to the existing homogeneous explosion theory, namely a practical definition of the critical condition, its calculation, and expressions for the available time before runaway in the case of a supercritical condition, taking into account the effects of natural convection inside the vessel and the reactant conversion. The extensions of the theory were confirmed by adiabatic and non-adiabatic runaway experiments on bench scale, and natural convection cooling experiments with liquids in various packages.