A water heating system is described. The water heating system comprises a vessel for holding water and for receiving heat from one or more heat sources for heating water in the vessel. The water heating system comprises a sensor comprising a plurality of temperature sensing elements for sensing a distribution of temperatures in the vessel. The water heating system comprises a connector for connecting the sensor to a retrofittable tank controller. The water heating system is configured to provide one or more characteristics of the water heating system to a retrofittable tank controller such that a retrofittable tank controller connected to the sensor and in receipt of the characteristics of the water heating system can determine from the distribution of temperatures in the vessel a quantity of useable heat stored in the vessel. A retrofittable tank controller for controlling a water heating system is also described. A sensor for measuring a temperature distribution of fluid within a vessel is also described.