An electrical-thermal co-simulation based on the finite element method is presented for analysis of high-power RF/microwave circuits. The co-simulation integrates a full-wave electromagnetic analysis and a transient thermal analysis through an iterative scheme, and is devised for the design and analysis of RF/microwave circuits operated at high frequencies and high power levels. To enhance the efficiency in solving large-scale problems, a domain decomposition scheme called the finite element tearing and interconnecting and an adaptive time-stepping scheme based on the algorithm of proportional-integral-derivative control are incorporated into the co-simulation. Temperature stability analysis is performed with the proposed co-simulation for a matching network in high-power RF amplifiers and for a substrate integrated waveguide filter.