We study theoretically phonon-assisted relaxation and tunneling in a system composed of a quantum dot which is coupled to a quantum well. Within the k·p method combined with the Löwdin elimination, we calculate the electron states. We calculate acoustic phonon-assisted relaxation rates between the states in the quantum well and in the quantum dot and study the resulting electron kinetics. We show that transition efficiency crucially depends on the system geometry. We show also that under some conditions, transition efficiency can decrease with the temperature.