Optimal synthesis of a heat-integrated water network (HIWN) accounts for the simultaneous conservation of energy and water resources. A significant amount of research work, ranging from complex nonlinear formulations to simplified linear models, has been carried out for the synthesis of HIVVNs. The incorporation of interception units leads to additional water and energy conservation but results in nonlinear formulations for heat integrated water regeneration network (HIWRN) synthesis. This paper proposes a linear mathematical formulation, based on the transshipment model, for the optimization of HIVVRNs using distributed interception units. As a result of a reduced number of variables and the absence of nonlinearities, the convergence efficiency is enhanced. The use of distributed interception units allows the regeneration streams to maintain their temperatures, thereby saving a significant amount of energy. A three-stage sequential approach and a simultaneous strategy are proposed for HIWRN synthesis. Although the simultaneous solution strategy provides cost optimal results, the three-stage sequential strategy is preferred in areas dealing with water scarcity and intermittent supply. The solution strategy is applicable to single as well as multiple-contaminant problems for single pass interception units with a fixed outlet and fixed removal ratio (RR). The methodology is demonstrated through literature examples for both types of interception units.