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We present an analysis of the thermal response of a hot-wire electroexplosive device (EED) excited with different transient signals. First-order and second-order analytical models to calculate the thermal response of an EED are assessed taking as reference numerical simulations obtained using ANSYS. For the early-time response, when the time is much smaller than the thermal constant of the EED, the best approach corresponds to a first-order differential model in which the thermal capacitance is calculated with short-pulse excitations. A linear simplification to calculate the maximum temperature due to short excitations is also shown to be adequate. On the other hand, the most appropriate model for the late-time response is a second-order model. The models are used to assess the electromagnetic susceptibility of a wired EED for different electromagnetic pulsed environments. Radiated signals produced by a mesoband radiator, two types of radars, and a hyperband radiator are considered. The radar signal proved to be the most disturbing source because of its highest duty cycle and its flat spectral response around a specific frequency. Even the temperature firing threshold can be exceeded with the radiated field produced by a radar of 200 kW of output power located at a distance of 5 m.