A method of manufacturing a porous ceramic part, comprising the following steps in succession: a) preparing a mixture M containing a ceramic powder in suspension, at least one gelling agent and at least one foaming agent, at a mixing temperature which is higher than the gelling temperature of the gelling agent; b) shearing the mixture M at a foaming temperature which is higher than the gelling temperature, to obtain a foam; c) gelling the foam by cooling the mixture M to a temperature below the gelling temperature of the gelling agent; and d) drying the gelled foam to obtain a perform. According to the invention, a stabilizing agent is added to the mixture M, which agent has an instantaneous viscosity, in Pa·s, that increases by a factor of at least ten when a shear rate of the stabilizing agent is reduced from 100 s−1 to 0.