Most studies assessing the safety of hot bridge wire EEDs employ temperature sensors that directly use the measurements of the temperature measurement device without analyzing the accuracy of the temperature measurement. This study establishes the response function of the exposed bridge and exposed bridge temperature rise system of hot bridge wire EEDs through the Rosenthal’s temperature rise equation and Laplace transformation as well as experimental tests, and through the response function, the response law and numerical characteristics of the two are compared and analyzed under four typical excitations. Under steady current injection and continuous-wave radiation, both exposed bridge and exposed bridge temperature measurement systems can reach thermal equilibrium, and the equilibrium temperature of both are the same. However, under pulse excitation, the temperature rise measurement value is significantly different from the actual value due to the large difference in response time of the exposed bridge (1 ms) and the exposed bridge temperature measurement device (0.82 s). Studies have shown that under steady current injection and continuous-wave radiation, temperature rise measurements can be directly applied to the safety assessment of hot bridge wire EEDs, while under pulsed conditions, temperature rise measurements cannot be directly applied.