In the 3+1 neutrino scheme with an additional state, we consider the thermalisation of neutrinos in the early Universe in the so-called very low reheating scenarios. This process could be incomplete due to the lack of interactions, leading to a reduced contribution of neutrinos to the cosmological energy density of radiation. We calculate this contribution, usually measured in terms of the parameter effective number of neutrino species ($N_{\rm eff}$), taking into account the full $4\times 4$ neutrino mixing matrix, as a function of the reheating temperature $T_{\rm rh}$.