The operating conditions of coal-fired power units are changing because of the current shift in the approach to technologies based on fossil fuels. Due to decarbonization issues, their function is now more often to balance shortages of electricity generated from renewable sources. A substantial rise can be observed nowadays in the significance of the capability of all the installation modules to operate under variable loads. One of the solutions improving the coal-fired power unit flexibility is the twin-boiler concept based on using a system with twin-boilers co-operating with one steam turbine. Such a solution makes it possible to obtain characteristics similar to gas-steam systems and achieve low values of the minimum load on the basic fuel. The solution operating characteristics cannot be determined fully unless issues related to the thermal and stress states of individual elements are discussed first. The subject of the numerical analyses presented in this paper are thermal and stress states arising in the elements of a turbine co-operating with 2 boilers during steady- and unsteady-state operation. Results of numerical simulation of the turbine steady operation, the start-up process and power change are presented. An analysis is conducted of the impact of the rate of changes in power on the level of stresses in the turbine elements and in consequence on the fatigue of the turbine rotors.