We analyse the reheating in the modification of $ν$MSM (Standard Model with three right handed neutrinos with masses below the electroweak scale) where the sterile neutrino providing the Dark Matter is generated in decays of the additional inflaton field. We deduce that due to rather inefficient transfer of energy from the inflaton to the Standard Model sector reheating tends to happen at very low temperature, thus providing strict bounds on the coupling between the inflaton and the Higgs particles. This in turn translates to the bound on the inflaton mass, which appears to be very light $0.1GeV \lesssim m_I\lesssim 10GeV$, or slightly heavier then two Higgs masses $300GeV \lesssim m_I\lesssim 1000GeV$.