The present invention is related to devices for evaporating volatile substances in a closed environment, without the use of electric power, heating elements or absorption wicks, for the purpose of simplifying and maximally reducing the cost of the device, but at the same time maintaining its efficacy and also allowing the user to be able to adjust at will the degree of evaporation of said product. For that purpose, the evaporator device uses a vapor permeable membrane as the element responsible for causing the evaporation of the product to be evaporated. The device is especially intended to be used with the cooperation of an air current with a suitable temperature enhancing the evaporation and diffusion of the volatile substance, such as the ventilation air outlet of a vehicle, for example. The volatile substance consists in an air-freshening product, insecticide or the like. The invention is also related to a method for the evaporation of volatile substances through a membrane.