Modern day District Heating and Cooling (DHC) networks are complex interconnections of heat energy sources and heat energy consumers wherein the available energy from the sources is networked to the consumers for meeting their space heating (or cooling) requirements. Often, the energy sources are renewables and thermal run-off from industrial processes which are intermittent. Under extremely exigent conditions (such as very low ambient temperatures), these DHC networks may potentially suffer from energy supply inadequacy. Subsequently, selfish uncoordinated control of heat energy inflow at distributed consumer premises can lead to unfair allocation of the already inadequate energy to different consumers, potentially leading to consumer disgruntlement. Factors such as thermal losses in the network, varying levels of building insulation and different building heat capacities only exacerbate these issues. In this paper, we propose a policy for implementing Demand Response (DR) in DHC networks with an objective of optimizing different fairness based objectives. Specifically, our proposed algorithm estimates dynamically evolving building thermal parameters from continuously recorded temperature sensor measurements from different points in the network. It then uses this knowledge to suggest suitable control of network parameters such as mass flow rate of fluid to the buildings in order to realize the network level thermal fairness based objectives.