We theoretically investigate dc electron resonant tunneling through an impurity state in a quantum well assisted by hot acoustical phonons. Numerical results for the tunneling current, obtained by nonequilibrium Green functions, reflect the hot-phonon-induced change in the spectrum and population of the impurity state. The induced change of the I-V characteristics has a typical two-peak form, which for larger populations of the level becomes distorted by increased intralevel phonon emissions. A qualitative agreement with experiments is obtained. ͓S0163-1829͑98͒04224-6͔Here c k,␣ϭL,R ϩ (c k,␣ϭL,R ) and E k,␣ϭL,R are creation ͑annihila-tion͒ operators and energies for electrons in the left (L) and right (R) reservoirs, d † ͑d͒ and E 0 describe the same for the level and ␥ k,␣ϭL,R are the coupling parameters between the level and the reservoirs. The operators b q † (b q ) and energies ប q ͑isotropic͒ describe acoustic phonons coupled by the interaction matrix elements M (q) to the electrons on the level. The structure factor F(q) is a square of the donor wave function transformed in a momentum representation.