An unusual type of oscillatory, thermal instability in a reaction which takes place in a semi-batch reactor, (i.e., when one reactant is admitted slowly to the reaction vessel and mixes with another reactant already present in the system) is investigated experimentally and theoretically. We show not only that oscillatory temperature changes may occur that are sufficiently large to constitute a formidable explosion hazard but also that the conditions under which such a hazard may take place could be entered unwittingly, in a mistaken belief that a move away from a potentially hazardous zone is being made. The theoretical background is formulated analytically in the context of a first order exothermic reaction. However, from the experimental study of the exothermic gaseous reaction between hydrogen and chlorine, we confirm the existence of oscillations and we show that the main features predicted by the simple theory transpose to more complex kinetic systems. In this particular system, temperature changes in excess of 200 K were measured in the unstable oscillatory region. The experimental study is linked to the theoretical foundations through numerical modelling of the non-isothermal process, based on a detailed kinetic mechanism of the H2 + Cl2 reaction. Similar oscillatory phenomena are also shown by numerical simulation to be possible in a semi-batch reactor in an exothermic reaction between two liquids.