Electro-explosive devices (an electric resistance encapsulated by a primary explosive) fundamentally convert electrical energy into thermal energy, to start off an explosive chemical reaction. Obviously, the activation of those devices shall not happen by accident or, even worse, by intentional exogenous influence. From an ordinary differential equation, which describes the electro-explosive thermal behavior, a remarkable, but certainly not intuitive, dependence of the temperature response on the time constant of the heat transfer process is verified: the temperature profile dramatically changes as the time constant spans a wide range of values, from much lesser than the pulse width to much greater than the pulse period. Based on this dependence, important recommendations, concerning the efficient and safety operation of electro-explosive devices, are proposed.