A process for the incineration of particulate solids, especially biological waste matter with low caloric value, feeds the solids into a combustion chamber of a furnace together with a sub-stoichiometric amount of fresh air to control the rate of combustion and to inhibit the formation of sintered ash. The furnace for implementing the process can be a cyclone furnace having a primary combustion chamber with a first feed inlet for the solids and air and a second air inlet positioned between the first inlet and an exhaust gas outlet. A supply tube extends through the exhaust gas outlet of the primary combustion chamber to supply a source of fresh air at ambient temperature to maintain the primary combustion chamber at a desired temperature. The fresh air maintains the furnace temperature at least at about 850° C. and generally at about 850° C. to less than about 1100° C. A source of fresh air at ambient temperature can also be directed into the primary combustion chamber through an annular air passage surrounding the exhaust gas outlet of the primary combustion chamber. The less than stoichiometric amount of air and the secondary air maintains the furnace at a sufficiently lower temperature to inhibit sintering of the solids.