The reaction of aluminium oxidation is exothermal and one of the main problems in anodizing is cooling of the anode surface. At room temperature, intensive stirring and low current densities are needed but even then, especially because of the low current density, the outer part of the oxide film will react with the electrolyte to form hydroxides. As a result, the superficial hardness will be reduced. You can introduce your cell into a larger vessel with ice water and try to anodize at current densities of about 4 A/sq.dm.