In order to fight global warming, most countries now develop ecological heating modes, among which district heating networks, often supplied with clean energy. However, the percentage of the population served by a district heating network remains very low in many countries. While district heating networks have the technical features of a natural monopoly, the goal of this paper is to improve the understanding of the actual market structure of district heating networks, taking into account specific constraints shaped by legal norms. We then consider the implications in terms of regulation of the district heating networks market in particular, but also in terms of public policy related to the heating market in general, highlighting the crucial role of public authorities.