The invention relates to a process for preparing a gelled, dried composition forming a monolithic aerogel with a heat conductivity of less than or equal to 40 mW·m−1·K−1 and derived from a resin of polyhydroxybenzene(s) and formaldehyde(s), to this aerogel composition and to the use thereof. This process comprises: a) polymerization in an aqueous solvent of said polyhydroxybenzene(s) and formaldehyde(s) in the presence of an acidic or basic catalyst, to obtain a solution based on the resin, b) gelation of the solution obtained in a) to obtain a gel of the resin, and c) drying of the gel to obtain a dried gel. According to the invention, step a) is performed in the presence of a cationic polyelectrolyte dissolved in this solvent, and the process also comprises a step d) of heat treatment under inert gas of the dried gel obtained in step c) at temperatures of between 150° C. and 500° C. to obtain the non-pyrolyzed aerogel whose heat conductivity is substantially unchanged, even after exposure to a humid atmosphere.