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We analyze the high-temperature continuous-wave performance of 1.3-μm AlGaInAs/InP laser diodes grown by digital alloy molecular-beam epitaxy. Commercial laser software is utilized that self-consistently combines quantum-well bandstructure and gain calculations with two-dimensional simulations of carrier transport, wave guiding, and heat flow. Excellent agreement between simulation and measurements is obtained by careful adjustment of material parameters in the model. Joule heating is shown to be the main heat source; quantum-well recombination heat is almost compensated for by Thomson cooling. Auger recombination is the main carrier loss mechanism at lower injection current. Vertical electron escape into the p-doped InP cladding dominates at higher current and causes the thermal power roll-off. Self-heating and optical gain reduction are the triggering mechanisms behind the leakage escalation. Laser design variation is shown to allow for a significant increase in the maximum output power at high temperatures.