Abstract: In a high-temperature furnace such as a heating furnace, a melting furnace or a blast furnace, a cooling cell assembly of a ferromagnetic material such as iron is used in the furnace wall. The thickness of the cooling cell assembly can be detected by winding primary and secondary windings about an iron core, passing an alternating current through the primary winding and inserting a sensor in an inspection hole for detecting the current or voltage induced in the secondary winding, forming a magnetic circuit in the sensor and a portion of the furnace wall, and detecting variations in magnetic permeability between the cooling cell assembly and mortar, refractory bricks or air gaps.