Heating consumes almost 50% of the global final energy consumption but only 10% of the heat supply is from renewable energy sources (RES). Rooftop solar collectors generate low temperature heat, which can be stored as sensible heat over many months. This can lower the use of oil boilers in winters, thereby playing an important part in decarbonisation. This paper examines the feasibility of using tank thermal energy storage (TTES) for decarbonising heating. It simulates hourly energy flows and compares different heating systems in 50 and 200 dwellings in multi-family households at Geneva, Switzerland. Hourly energy flows for four different heating systems configrations, viz. oil boiler, solar collector with TTES, solar collector with TTES & heat pump, and a system having only a centralised air-water heat pump are simulated. Various performance indicators such as levelised cost of heat, percentage share of RES, peak electricity load and cost of decarbonisation are evaluated. Sensitivity of perfomance indicators to head demand, heat supply and heating network temperature is examined. Results show that a heating system having only a centralised air-water heat pump is the best option, but CO2 emissions cannot be eliminated. On the other hand, in case of low heat demand (due to building renovation and lower heating network temperature in future), use of TTES with solar collectors could lead to a higher share of RES. Further, the peak electricity load is much lower and heating can be completely decarbonised. Thus, TTES has an important role to play in decarbonisation of heating, albeit at a higher cost.