In this paper, electrical heat engines driven by the Johnson-Nyquist noise of resistors are introduced. They utilize Coulomb's law and the fluctuation-dissipation theorem of statistical physics. In these engines, resistors, capacitors and switches are the building elements. For best performance, a large number of parallel engines must be integrated to run in a synchronized fashion, and the size of an elementary engine must be at the 10 nm scale. At room temperature, in the most idealistic case, a two-dimensional ensemble of engines of 25 nm size integrated on a 2.5 2.5 cm silicon wafer with 10 C temperature difference between the warm-source and the cold-sink would produce a power of about 0.5 W. Regular and coherent (correlated-cylinder states) versions of these engines are shown and both of them can operate in either four-stroke or two-stroke modes. In the idealistic case, all these engines have Carnot efficiency, which is the highest efficiency possible in any heat engine without violating the second law of thermodynamics. 2011 Elsevier Ltd. All rights reserved.