We propose an electrically pumped laser diode based on multiple HgTe quantum wells with band structure engineered for Auger recombination suppression. A model for accounting for hot phonons is developed for calculating the nonequilibrium temperature of electrons and holes. Using a comprehensive model accounting for carrier drift and diffusion, Auger recombination and hotphonon effects, we predict of lasing at \(\lambda \sim 3 \) \(\mu\)m at room temperature in 2.2 nm HgTe/Cd\(_{0.85}\)Hg\(_{0.15}\)Te quantum well heterostructure. The output power in the pulse can reach up to 600 mW for 100 nanosecond-duration pulses.