Reverse osmosis (RO) is one of the most widely employed technologies for water desalination. A drawback of this technology is high consumption of electricity by electric motors used for high-pressure water pumping. Energy consumption can account for up to 70% of the desalination costs. Due to the high energy intensity the carbon footprint of desalination processes is substantial. Modern seawater desalination RO plants emit between 1.4 and 1.8 kg CO2 per cubic meter of produced water. High capital costs due to expensive high-pressure water pumps and concentrate water energy recovery systems such as pressure exchanges, or Pelton turbines is another drawback. Most of pumps and compressors including those used in RO desalination plants are driven by electric motors or internal combustion engines (diesels, gas turbines). Therefore compression and pumping are always associated with multiple energy transformations. Pumping systems account for nearly 20% of the world’s electrical energy demand and range from 25-50% of the energy usage in certain industrial plant operations. To improve economics of water desalination plants we propose innovative energy efficient, inexpensive, robust water pump powered by heat. The basic principle of the pump (or engine) is the same as that of regenerative type external combustion engines with closed cycle – working fluid expands when it is heated and contracts when it is cooled. Regeneration of heat makes pumps of this type very energy efficient. The novelty of the pump comprises a new working cycle in combination with the use of a dense working fluid which is liquid in the cold space of the pump and gas or supercritical fluid in the hot space of the pump. The working fluid of the engine has very high thermal expansion, yet low compressibility when it is in liquid phase. Carbon dioxide, water-alcohols mixtures or mixtures hydrocarbons can be used as the working fluids. A distinguishable feature of the pump proposed is its simplicity. It does not have any high precision parts and even does not require super alloys and any other expensive materials. The working fluid in the engine is compressed by heat and the energy of the working fluid is directly transmitted to a liquid to be pumped. The pump can generate very high pressures (hundreds bars) and therefore can be used instead of modern plunger pumps driven by electric motors, thus eliminating completely the consumption of electricity for pumping in RO processes. Another important feature of the pumps is that no high temperature heat sources are needed. Heat sources with temperature of 200 – 300 0C could be sufficient to create pressure drops typical of RO processes. Therefore different sustainable and renewable energy sources such as solar radiation, waste heat, and geothermal energy can be used to power the pump.