Process for producing a thermally insulating mixture comprising hydrophobic silica, in which a) a pulverulent carrier material selected from the group consisting of precipitated silicas, SiO2 aerogels, pearlites and mixtures thereof is coated with a liquid silicon compound, where the liquid silicon compound has at least one alkyl group and a boiling point of less than 200° C., and b) the pulverulent carrier material that has thus been coated with the liquid silicon compound is mixed with a composition comprising a pulverulent hydrophilic fumed silica and the mixture is subjected to thermal treatment at more than 40° C. and c) any unreacted silicon compound is subsequently removed from the thermally treated mixture, thus giving the thermally insulating mixture comprising hydrophobic silica.