This research presents technical and cost-minimised design to decarbonise the heating network by using large-scale heat pump and thermal heat storage. In this paper, real hourly heat-consumption and heat production cost data for the city of Aarhus, Denmark are used for calculating techno-economic feasibility of coupling the heating network with electrical grid. An optimum solution is suggested for the entire network with least amount of backup generation capacity, thermal heat storage capacity, natural gas boiler capacity and levelised cost of energy. Aarhus constitutes 5% of the Denmark's total heat demand and 4% of electrical load demand. This can be fulfilled with 160 MW of rated wind generation capacity, 35 MW of solar PV generation capacity, 45 MW of backup generation capacity, 221 MW of natural gas boiler capacity and 3.4 GWh of thermal heat storage capacity. The levelised cost of energy shows that, the coupling between the electrical grid and heating sector reduces the cost by more than 50% to 45 /MWh. However, the cost-minimised design is possible with wind/solar mix of 85% and renewable energy penetration of 100%. Sensitivity analysis concedes that, the 100% decarbonisation of heating sector relies heavily upon the cost assumed for wind generation and solar PV generation, instead of the operation and maintenance cost for heat pump. Furthermore, the reduction in cost for wind generation and solar PV generation leads to the decrease in levelised cost of energy. Whereas, the reduction in cost for heat pump, thermal heat storage capacity and natural gas boiler capacity leads to an increase in renewable energy penetration. Sensitivity analysis further reveals that, increasing thermal heat storage capacity and the cost of selling excess renewable energy does not have major impact upon the levelised cost of energy and can be instrumental for the economic viability of fossil-free future. (C) 2018 Elsevier Ltd. All rights reserved.