The temperature sensitivity of the threshold current of 1.3 micrometer semiconductor lasers, denoted by the characteristic temperature T0, has remained low, with values ranging from 40 K up to a maximum of order 100 K. We report here on a combined theoretical and experimental analysis to identify the dominant factors contributing to this poor temperature sensitivity. We have determined directly the temperature dependence of the radiative current density, Jrad, by measuring the integrated spontaneous emission, L, from bulk and strained quantum well buried heterostructure devices. We find an effective T0 for Jrad of around 200 K for the bulk device and around 300 K for the quantum well device, in good agrement with the theoretical prediction for ideal lasers. This radiative temperature dependence compares with the measured T0 of around 50 - 60 K for the total threshold current density in both devices, from which we conclude that radiative recombination is not the dominant mechanism of the temperature sensitivity of the laser. We also find from the spontaneous emission data that just below threshold L varies with current I as I varies direct as L3/2, which is expected in the Boltzmann approximation if auger recombination is the dominant current path. We have used these findings to estimate T0 from as simple analytic expression we have derived and find values at room temperature of 40 - 100 K, in agreement with experiment. This poor T0 results both from the temperature dependence of the differential gain and by the major contribution of auger recombination to the total threshold current.