Typical domestic induction cooktops can only heat ferromagnetic pots/vessels. However, to increase the availability and marketability of induction heating (IH) cooktop products, heating techniques for all types of metallic pots (i.e., created from metals such as aluminum, copper, and stainless steel) are required. To satisfy the requirements of induction cooktops, this paper proposes the design of an all-metal domestic IH system that can heat any type of metallic pot while considering the temperature variation of the working-coil. A control algorithm using a power curve-fitting method (CFM) is presented to quickly respond to load parameter variations in the IH. In addition, the CFM control algorithm is established to compensate for the power reference value by reflecting the increase in the working-coil temperature during the heating of the non-ferromagnetic pot. To evaluate the performance of the proposed system, the control algorithm strategy and experimental results based on a 3.2 kW all-metal IH cooktop are presented.