A portable catalytic combustion heater, wherein fuel vapor (11) and air (10) are supplied to a catalyst (6) which promotes the flameless combustion of fuel and releases that. The fuel is supplied as a liquid, passes through a selectively permeable membrane (8) such that fuel vapor exits the membrane and is fed to the catalyst (6). Additional features include porous supports and means of enhancing and diminishing the catalytic rate of combustion and controlling the heat output.