Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is considered. This is a new problem in thermal explosion theory, not previously considered in a distributed system formulation, but important for combustion and fire science. It describes autoignition of wide range of fires (such as but not limited to piles of biosolids and other organic matter; storages of munitions, explosives, propellants) subjected to temperature variations, such as seasonal or day/night variation. The problem is considered in formulation adopted in classical studies of thermal explosion. Critical conditions are determined by frequency and amplitude of ambient temperature oscillations, as well as by a number of other parameters. Effects of all the parameters on critical conditions are quantified. Results are presented for the case of planar symmetry. Development of thermal explosion in time is also considered, and a new type of unsteady thermal explosion development is discovered where thermal runaway occurs after several periods of temperature oscillations within the medium.