This paper presents a test stand for the capture of CO₂ from flue gases arising due to firing pulverised hard coal. The stand, financed from the 2014–2021 Norway Grants, is installed at a Polish power plant. The innovation of the proposed CO₂ capture method, developed by the Norwegian partner in the project (SINTEF Industry), lies in the use of activated carbon in the process of temperature swing adsorption in a moving bed. The paper also presents preliminary results of numerical simulations performed using the General PROcess Modelling System (gPROMS) software. The simulations concerned the operation of a supercritical power unit combined with a system for capturing CO₂ from flue gases. Transient operation of the system was analysed, assuming rapid changes in the power unit load. Special attention was paid to the CO₂ capture process energy consumption at an increase in load by 5% of the power unit nominal capacity in 30 s. It is found that the proposed CO₂ capture method “keeps up” with such rapid load changes at the method energy consumption smaller than 2 MJ/kg CO₂.