In a thermal explosive reaction, the rate of reaction varies rapidly with temperature and the moment of explosion occurs at some finite temperature v d . The reaction rate usually follows the Arrhenius law over a certain range of temperature [v 0 , v 1 ] with v 1 v d . A quenching model is discussed here to account for the thermal explosion. This model gives a better approximation than the blow-up model for the Arrhenius law over the range of temperature [v 0 , v 1 ] and describes the rate of the thermal explosive reaction beyond v 1 to v d .