Wein’s law is not too much help here as we are seeing just the tail of the black body distribution and stars like these are not really black bodies in any case due to the contribution of the deep absorption lines which varies with temperature
Looking at the Pickles standard spectra (see attached) The change in Betelgeuse looks to correspond to a change in spectral class of around 1-1.5 points eg M2 to M3.5 That is equivalent to a drop in Teff of around 200-300K
