The invention relates to a method for producing phosphoric acid, including: attacking phosphate rock by means of sulfuric acid between 70° and 90° C. with formation of a first calcium sulfate dihydrate crystal slurry, the aqueous acid phase of said slurry having free P2O5 content between 38 and 50 wt % and free SO3 content that is less than 0.5 wt % and greater than 0.05 wt %; converting said first slurry by means of heating at a temperature greater than 90° C., thus giving rise to a second slurry formed of calcium sulfate hemihydrate crystals; and, within the second slurry, separating a produced phosphoric acid, having a free SO3 content that is less than 2%, and a calcium sulfate hemihydrate filter cake.