In heat networks, energy storage in the form of hot water in a tank is a viable approach to balancing supply and demand. In order to store a desired amount of energy, both the volume and temperature of the water in the tank need to converge to desired setpoints. To this end, we provide a provably correct internal model controller that guarantees these tracking goals and is robust against parameter uncertainties. In order to design this controller and analyze the closed-loop system, we derive a nonlinear model from first principles. This model describes the temperature and volume dynamics of a setup consisting of a single producer with a storage tank and multiple consumers. We show that the control goal can be achieved by measuring only the aggregated flow rate of the consumers, the volume of the storage device, and the corresponding temperature.