Cosmetic dispersions comprising an aqueous phase and an oily phase, the aqueous phase containing a polymer comprising water-soluble units and units with an LCST, wherein the LCST units an have in water a demixing temperature of from 5 to 40.degree. C. for a concentration of 1% by mass is used, the polymer being present in a concentration such that the gel point of the aqueous phase is from 5 to 40.degree. C., to ensure the stability of the dispersions at temperatures from 4.degree. C. to 50.degree. C.