Device-performances of 3.7 THz indirect-pumping quantum-cascade lasers are demonstrated in an InGaAs/InAlAs material system grown by metal-organic vapor-phase epitaxy. The lasers show a low threshold-current-density of ~420 A/cm2 and a peak output power of ~8 mW at 7 K, no sign of parasitic currents with recourse to well-designed coupled-well injectors in the indirect pump scheme, and a maximum operating temperature of Tmax ~100 K. The observed roll-over of output intensities in current ranges below maximum currents and limitation of Tmax are discussed with a model for electron-gas heating in injectors. Possible ways toward elevation of Tmax are suggested.