We suggest a production mechanism of sterile neutrino dark matter whose interaction with a thermal bath is feebler than required by the freeze-in mechanism. It relies on the non-adiabatic transition in the process of the resonant conversion of thermal particles to the dark matter state, which can occur at a temperature much higher than the dark matter mass. This can be accomplished for a wide range of the sterile neutrino masses, from keV to TeV, with a judicious choice of their self-interacting couplings