Assuming a bi-Maxwellian electron energy distribution function, the temporal and radial distribution of the electron temperature is determined in nanosecond pulsed longitudinal discharges used for excitation of two prospective high-power gas-discharge lasers, namely, a deep ultraviolet Cu+ Ne-H2-CuBr laser and a He-Sr+ recombination laser. For this purpose, the parameters of the set of nonstationary heat-conduction equations for the two groups of electrons, namely, the electrical power density and the specific heat capacity, are determined for each group. A 2D(r,t) numerical model is also developed in order to solve the set of the equations.