The Morin transition of very thin Ir-doped alpha-Fe2O3 films, which is not detectable with conventional magnetization measurements, was studied by conversion electron Mossbauer spectroscopy using a Co-57 source and nuclear resonant scattering using a synchrotron light source. It was found that (i) the Morin transition temperature increases as the Ir ratio increases, (ii) it decreases when the film thickness decreases, and (iii) the transition becomes irreversible when Ir ratio is small and the thickness is thin. These tendencies were found reproducible and systematic, although the mechanisms are to be clarified by further studies.