A process for controlling a high temperature electrolyzer in which the one or more stacks of cells are arranged in an enclosure pre-heated to a high temperature and thermally insulated, where the electrolyzer is connected to an electric energy source for its power supply in order to implement an electrolytic reaction and where the process includes: monitoring of the power supplied by the energy source; redirecting upstream of the electrolyzer a portion of the power supplied by the energy source in order to heat the one or more stacks of cells when the value of the power supplied becomes lower than a previously set limit value; otherwise, no redirecting. A process for production of hydrogen or syngas incorporating the above driving process, where a driving system implements the above driving process and a hydrogen production system implements the corresponding hydrogen production process.