In the further advancement of the energy transition towards renewable energy sources, a significant role can be played by energy storage systems. A relatively new energy storage technology is the reversible solid oxide cell. A reversible solid oxide cell is an electrochemical device that can operate as an electrolyser to produce a fuel from electricity, and as a fuel cell to produce electricity from fuel. At Delft University of Technology, a hydrogen and oxygen fuelled solid oxide fuel cell and gas turbine integrated system has been designed. In order to redesign this solid oxide fuel cell and gas turbine integrated system into a reversible solid oxide cell system, the design of a solid oxide electrolyser system is required. One of the main challenges when designing a solid oxide electrolyser system is the heat requirement of the system. However, little research on the design of solid oxide electrolyser systems has yet focussed on thermal optimization of the system. In this thesis, three solid oxide electrolyser systems, displaying different heat integration layouts, were designed and examined. The results show that the highest energy and exergy efficiencies, respectively 75.52% and 75.42%, are obtained by the solid oxide electrolyser system that evaporates the water in the system using the heat that is generated by the hydrogen and oxygen storage compression. This solid oxide electrolyser system is combined with the solid oxide fuel cell and gas turbine integrated system to design a reversible solid oxide cell system. A round-trip energy efficiency, based on the lower heating value of hydrogen, of 48.40% is reached by this reversible solid oxide cell system.