Reverse osmosis (RO) is a desalination technique that is commonly preferred because of its low energy consumption. In this paper, an innovative, thermally powered RO desalination process is presented. This new thermo-hydraulic process uses solar thermal energy in order to realize the pressurization of the saltwater beyond its osmotic pressure to allow its desalination. This pressurization is enabled thanks to a piston or a membrane set in motion in a reservoir by a working fluid that follows a thermodynamic cycle similar to an Organic Rankine Cycle. In this cycle, the evaporator is heated by low-grade heat, such as the one delivered by flat-plate solar collectors, while the condenser is cooled by the saltwater to be treated. Such an installation, designed for small-scale (1 to 10 m3·day−1) brackish water desalination, should enable an average daily production of 500 L of drinkable water per m² of solar collectors with a specific thermal energy consumption of about 6 kWhth·m−3. A dynamic modeling of the whole process has been developed in order to study its dynamic cyclic operating behavior under variable solar thermal power, to optimize its design, and to maximize its performances. This paper presents the preliminary performance results of such a solar-driven desalination process.