The invention relates to a method for preparing a gelled, dried composition that forms a monolithic aerogel having heat conductivity less than or equal to 40 mW.m-1.K-1 and is made from a resin made of polyhydroxybenzene(s) and formaldehyde(s). The invention also relates to said aerogel composition and to the use thereof. Said method includes: a) polymerizing, in an aqueous solvent, said polyhydroxybenzene(s) and formaldehyde(s) in the presence of an acid or base catalyst so as to obtain a solution made from said resin; b) gelling the solution resulting from Step a) so as to obtain a gel from the resin; and c) drying the gel so as to obtain a dried gel. According to the invention, Step a) is implemented in the presence of a cationic polyelectrolyte dissolved in said solvent, and the method also includes a Step d) for heat-treating, under inert gas, the dried gel resulting from Step c) at temperatures between 150 DEG C et 500 DEG C so as to obtain the non-pyrolyzed aerogel having heat conductivity that is substantially unchanged after exposure to a humid atmosphere.