District heating (DH) networks are complex thermal grids wherein a centrally heated fluid is circulated through a network of pipes and heat exchangers to meet the heating needs of residential and commercial buildings. Several factors can lead to inefficient and unfair energy distribution among consumers in these networks. These include varying levels of building insulation, distance of individual buildings from the central energy source, and thermal losses in network pipes. Moreover, shortage of energy at the central energy source and extreme weather conditions can exacerbate these issues, leading to differing levels of thermal comfort and customer disgruntlement in the long run. In this paper, we propose and study a demand response scheme that attempts to ensure thermal fairness among energy consumers in modern thermal grids. We develop optimization formulations based on thermodynamic models of DH networks, which determine optimal energy flow for individual buildings in order to achieve thermal fairness across the network. Our numerical results using physics based models for DH networks show that it is indeed possible to achieve network level thermal fairness based objectives by controlling network parameters such as mass flow rates of water to the consumer premises and the supply water temperature.