A cellular structure thermal insulation material includes by weight as compared to the material total weight: from 4 to 96% of a hydraulic binder, which prior to being contacted with water, includes at least one phase selected from C3A, CA, C12A7, C11A7CaF2, C4A3$ (Yee lemite), C2A(1-x)Fx (where x belongs to [0, 1]), hydraulic amorphous phases having a C/A molar ratio ranging from 0.3 to 15 and such that cumulated amounts of Al2O3 of these phases be ranging from 3 to 70% by weight of the hydraulic binder total weight, from 4 to 96% of at least one filler, the material having a pore volume ranging from 70% to 95%. The use of a mineral foam for making thermal insulation material as well as methods for making the mineral foam are also described.