The transverse flux heating (TFH) concept offers very high electrical efficiency in combination with unique technological flexibility. Numerous advantages make this method beyond competition to be applied in e.g. continuous strip production and processing lines. However, all potential advantages of TFH can be realized in practice only by optimal design of the inductor shape and optimal control of the heaters, using numerical modelling and optimization techniques. The paper describes a successive approach to optimal design of a single layer induction coil, which will be used for onesided TFH of moving thin steel strip with constant width. The peculiarity of the design refers to the very slow movement speed of the strip and the target temperature, which is set below Curie.