Explored the area of distribution of heat energy for district heating and area of Lean to see what changes and improvements can make the introduction of Lean thinking in energy management of this activity. It describes the basic features of the distribution of heat energy, highlight the problems that affect the ineffectiveness of activities and set objectives of the research. Based on the knowledge and examples presented in scientific papers in the field of heat energy distribution are analyzed activities that contribute most to the increase of energy efficiency and relevant indicators of the effectiveness of the distribution process (heat losses, water losses due to network updates and greenhouse gas emissions). The research papers in the field of Lean has served to analyze the applicability and determine the meaning of lean principles to district heating. Lean losses associated the corresponding losses in the distribution of heat energy. It appears that nearly all lean losses can be seen as a waste of energy, that is, with the loss of water and greenhouse gas emissions, one of the main green of losses. Based on the research model LEGREM-DHE is designed to monitor the efficiency of the process of distribution of heat energy by applying lean principles, which consists of the following steps: 1. Setting energy VSM map initial state distribution processes This raises the energy map of the VSM initial state of the process of distribution of heat energy in which the running baseline most important indicators of the effectiveness of these activities. 2. Analysis of the current value Showing and analyzes current value of energy efficiency in the distribution of heat energy, which is seen as a lean process consists of: activities that add value (VAT - Value Added Time) - activities that do not add value, but are required to perform the activity (Vat - Not Value Added Time) and - activities that represent a net loss of (WT - Waste Time). 3. Plans for process improvement They bring the plans to reduce losses, their optimization and increase efficiency in the distribution of heat energy. Responding lean tools and techniques are applied in the process of distribution of heat energy through the implementation of selected activities that contribute most to the reduction and elimination of losses in distribution. 4. Setting energy VSM map future state distribution processes This raises the energy VSM map of the future state of the process of distribution of heat energy with marked changes in the baseline and estimated (target) values of performance indicators that should be achieved after the improvement process. 5. Implementation of measures and actions to improve processes It stipulates the metrics for monitoring achievement of target values of the indicators of efficiency of the process, and then implemented the selected activities, continually evaluating and reviewing the performance of the set goals. Striving for continuous improvement of processes and specifying new targets continue the present process as the PDCA cycle so that the re-runs from the initial to the final step of the model. Thereby allows balanced achievement of the objectives which does not disturb the required process quality. Shaped model LEGREM-DHE has been tested on the district heating system in the city of Osijek. It analyzes how the reduction of lean losses (transport, waste and excessive heat generation), green losses (energy, water, flue gas emissions) and to increase the energy efficiency of the process of distribution of heat affects the application of appropriate lean tools and techniques through the implementation of the following activities: - revitalization of the district heating network (Standardization, Andon) - optimization of temperature and operation of the main circulation pumps hot water network (Poka-Yoke, Pull) - improving the quality of corrective maintenance (TPM, 5 Whys) - replacement of hot water network that shares a "bottleneck" developing heat consumption (Bottleneck Analysis) - reduction of heat energy consumption after installation of heat cost allocators and thermostatic radiator valves (Poka-Yoke). Lean and green metrics monitoring actual values of the most important indicators of the efficiency of the process of distribution of heat energy after the implementation of these activities shows that the application of lean principles can increase the efficiency of these activities and district heating systems, reduce primary energy consumption and greenhouse gas emissions that contribute to raising the quality of services and customer satisfaction connected to the heating system. The scientific contribution of this research is expressed through: - systematization of lean and green energy losses in the distribution of heat energy - setting energy VSM map for process heat energy distribution - design models for monitoring the efficiency of the process of distribution of heat energy and - development of new processes in the energy sector based on lean principles.