This paper deals with thermal ice protection of electrically heated restraining grids designed for applications in the environmental control system (ECS) of passenger aircraft. The restraining grids described in the paper consist of strung, electrically insulated wire and are - in certain operation modes of the ECS - exposed to an airstream containing supercooled water droplets and/or ice particles. Heat is generated in the wire by an electric current, and the temperature of the wire is controlled with the aid of an electronic control system. A substantial question for laying out the controller and for operating the grids is the following: What minimum heating power is required to prevent ice accretion on the surface of the wire, i.e., what is the least heating power that is necessary to keep a grid being exposed to specific icing conditions devoid of ice? This problem is studied for a simple model system first and is then examined for restraining grids. The methods utilized for these investigations include icing wind tunnel experiments, numerical simulations involving FH JOANNEUM's icing code ICEAC2D v2 as well as analytical calculations.