Process for manufacturing a thermally insulating material comprising the following steps: a) preparing an aqueous mixture of a solid mineral substance in suspension having a specific surface area S of greater than 5 m2/g; b) adding to the mixture at least one pore-forming agent; c) stirring so as to obtain a homogeneous mixture; d) preforming a substrate from the homogeneous mixture; e) optionally drying the substrate at least partially; f) removing, at least partially, the pore-forming agent; and such that said specific surface area S, expressed in m2/g and measured by BET, and the mean particle diameter Dpm of the pore-forming agents, expressed in micrometers and measured by dynamic light scattering, obey the relation: 1/S