Several studies have involved a combination of heat and gravitational energy exchanges to create novel heat engines. A common theoretical framework is developed here to describe thermogravitational cycles which have the same efficiencies as the Carnot, Rankine, or Brayton cycles. Considering a working fluid enclosed in a balloon inside a column filled with a transporting fluid, a cycle is composed of four steps. Starting from the top of the column, the balloon goes down by gravity, receives heat from a hot source at the bottom, then rises and delivers heat to a cold source at the top. Unlike classic power cycles which need external work to operate the compressor, thermogravitational cycles can operate as a “pure power cycle” where no external work is needed to drive the cycle. To illustrate this concept, the prototype of a thermogravitational electrical generator is presented. It uses a hot source of average temperature near 57 °C and relies on the gravitational energy exchanges of an organic fluorinated fluid inside a balloon attached to a magnetic marble to produce an electromotive force of 50 mV peak to peak by the use of a linear alternator. This heat engine is well suited to be operated using renewable energy sources such as geothermal gradients or focused sunlight.