Abstract District heating networks transport thermal energy from one or more sources to a plurality of consumers. Lowering the operating temperatures of district heating networks is a key research topic to reduce energy losses and unlock the potential of low-temperature heat sources, such as waste heat. With an increasing share of uncontrolled heat sources in district heating networks, control strategies to coordinate energy supply and network operation become more important. This paper focuses on the modeling, control, and optimization of a low-temperature district heating network, presenting a case study with a high share of waste heat from high-performance computers. The network consists of heat pumps with temperature-dependent characteristics. In this paper, quadratic correlations are used to model temperature characteristics. Thus, a mixed-integer quadratically-constrained program is presented that optimizes the operation of heat pumps in combination with thermal energy storages and the operating temperatures of a pipe network. The network operation is optimized for three sample days. The presented optimization model uses the flexibility of the thermal energy storages and thermal inertia of the network by controlling its flow and return temperatures. The results show savings of electrical energy consumption of 1.55%–5.49%, depending on heat and cool demand.