A process for operating a heater that can be operated with hydrocarbon fuel, especially for a vehicle includes providing a substoichiometric air/fuel mixture in a precombustion chamber (18) for a combustion operation and performing a cold flame combustion in the precombustion chamber (18). The precombustion products forming in the precombustion chamber (18) during the cold flame combustion are supplied to a catalyst arrangement (32) and a partial catalytic oxidation is performed for producing a gas containing hydrogen and carbon monoxide. The gas produced during the partial catalytic oxidation is supplied to a main combustion chamber (34) for producing a hydrogen/carbon monoxide/air mixture. The hydrogen/carbon monoxide/air mixture is burned in the main combustion chamber (34).

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