Abstract: The invention is directed to a heatable appliance for personal use, in particular a hair-care appliance, including a device for the flameless combustion of a fuel/air mixture and an associated activation device for initiating its flameless combustion, wherein the device includes a stable carrier structure 28 of a mass m.sub.T and a density s.sub.T. The carrier structure 28 is provided with a coating having a specific surface area O.sub.B (according to the BET method) and a mass m.sub.B, the coating carrying a catalytically active material of a mass m.sub.K. In order to ensure a high mechanical stability, a satisfactory activation ability and at the same time a high resistance to poisoning of the catalyst, the ratio ##EQU1## is set at values in the following range:0.3.times.10.sup.6 .ltoreq.delta.ltoreq.30.times.10.sup.6.