This invention discloses a portable catalytic combustion heater. Fuel vapor and air are supplied to a catalyst which promotes the flameless combustion of the fuel, releasing heat. The fuel is supplied as a liquid, passes through a selectively permeable membrane such that fuel vapor exits the membrane and is fed to the catalyst. Additional features such as porous supports and means of enhancing and diminishing the catalytic rate of combustion and controlling the heat output are also shown. This invention can be used to heat apparel, blankets, food, dwellings, containers, machinery, insect attractants, humidifiers, and perfume generators.