Two major causes of hardening and subsequent embrittlement in ferrite steels are the spinodal decomposition of the binary Fe-Cr solid solution and the carbide formation due to the presence of carbon as foreign interstitial atoms. In the present work, simulations of the microstructure evolution due to thermal ageing are performed by means of a kinetic Monte Carlo code and using a state-of-the-art interatomic potential based on density functional theory (DFT) predictions and experimental data. The main issues concern the possibility to perform thermal ageing simulations in an acceptable computational time frame and to reproduce a realistic behavior of carbon kinetics and carbide formation. The simulations on the binary system show the microstructural evolution during thermal ageing and allowed to find an exponential trend related to the acceleration as a function of temperature. With the insertion of carbon in the model, the chromium precipitation tends to accelerate. The carbon clustering, analyzed separately, is faster with higher C concentrations and in lattices with segregated chromium.