Abstract Several utility companies adopted time-based rates to encourage the customers to shift their consumption from high demand hours to those with lower demand. In this regard, the two most commonly used time-based rates are time-of-use (TOU) tariffs and critical peak pricing (CPP). Previously, various heat storage techniques were used in buildings to achieve peak load shifting. In this study, sensible heat storage (by electrically heated floors) is considered to bridge the temporal gap between energy supply and demand. To do so, the performance of energy storage was investigated during hours with lower electricity prices. In this way, the stored heat can be used later during hours when the electricity price is high to maintain thermal comfort. To operate heaters in the concrete slab a model free self-learning control (SLC) system was adopted as it can be widely applied in different houses with minor modification. In this study, a TRNSYS-MATLAB model was developed and validated using experimental data collected during winter 2017-2018. Simulations were conducted to investigate the peak shifting and heating cost-saving potential of the SLC system under TOU and CPP time-based rates of Ontario and Quebec, respectively. The results showed that the SLC system could achieve almost complete peak shifting (TOU: 97.6% and CPP: 99.8%) to reduce the stress on the electrical grid. Moreover, it could decrease the heating cost by about 17% and 21% for TOU and CPP, respectively. The SLC system was found to be more efficient for CPP compared to TOU time-based rates, since the former includes mid-peak hours. Overall, it is beneficial for both the supply as well as demand-side since the SLC system could achieve both peak shifting and heating cost savings.