By studying thermal behavior of all-MBE surface-emitting lasers, barrier heights and optimum cavity design parameters are obtained. The barrier heights for holes between hetero-interfaces of Al0.3Ga0.7As-Al0.65Ga0.35As and AlAsAl0.65Ga0.35As (DELTAx = 0.35) are measured to be 77 meV at zero bias for the deep-red top-surface-emitting laser. The barrier height decreases linearly with forward bias voltage, explaining the nonlinearity in current-voltage characteristics of the top-surface-emitting laser. The contribution of electrons to electrical resistance is estimated to be negligibly small compared to that of holes for the structure consisting of DELTAx = 0.35. Minimum threshold current and maximum differential quantum efficiency observed around 200 K indicates slight mismatch between gain maximum and Fabry-Perot resonance for the deep-red top-surface-emitting laser.