Fe(OH)3 can also be written as FeO(OH).H2O
I am speculating as I am no expert on the matter, but seen in line with the observation that iron 3 oxide forms out of iron hydroxyoxide by heating, I would expect that the crystallized water will evaporate first, followed by a recombination of 2 hydroxide ions into water and an oxide, with the evaporation of said water.
there is indeed no oxidation/reduction going on, just dehydration