We report on efficient spin injection in p-doped (In, Ga)As/GaAs quantum-dot (QD) spin light-emitting diodes (spin LEDs) under zero applied magnetic field. A high degree of electroluminescence circular polarization (P c) ∼19% is measured in remanence up to 100 K. This result is obtained thanks to the combination of a perpendicularly magnetized Co-Fe-B/MgO spin injector allowing efficient spin injection and an appropriate p-doped (In, Ga)As/GaAs QD layer in the active region. By analyzing the bias and temperature dependence of the electroluminescence circular polarization, we evidence a two-step spin-relaxation process. The first step occurs when electrons tunnel through the MgO barrier and travel across the GaAs depletion layer. The spin relaxation is dominated by the Dyakonov-Perel mechanism related to the kinetic energy of electrons, which is characterized by a bias-dependent P c. The second step occurs when electrons are captured into QDs prior to their radiative recombination with holes. The temperature dependence of P c reflects the temperature-induced modification of the QD doping, together with the variation of the ratio between the charge-carrier lifetime and the spin-relaxation time inside the QDs. The understanding of these spin-relaxation mechanisms is essential to improve the performance of spin LEDs for future spin optoelectronic applications at room temperature under zero applied magnetic field.