A method is disclosed to utilize the thermal energy from essentially limitless heat sources, such as the ocean or the atmosphere, and from limited heat sources, such as the combustion of fossil fuels, for power production. The fluid from such heat sources gives heat to the working medium of a prime mover by passing it through a first heat transport means. The effluent cooled source fluid from the first heat transport means is then used for removing the exhaust heat from the prime mover through a second heat transport means and can also be used for the purification of liquids by a freezing process. The first and the second heat transport means comprise various processes so devised that net work is produced at a significant rate by the power system and entropy is produced continuously in the surroundings. The limited heat source is optional.