  Flow and storage volume regulation is essential for the adequate transport
and management of energy resources in district heating systems. In this letter,
we propose a novel and suitably tailored -- decentralized -- adaptive control
scheme addressing this problem whilst offering closed-loop stability
guarantees. We focus on a system configuration comprising multiple heat
producers, consumers and storage tanks exchanging energy through a common
distribution network, which are features of modern and prospective district
heating installations. {\color{black}The proposed controller is based on
passivity, backstepping and (indirect) adaptive control theory.
