A controller for a temperature management system for heating and/or cooling a room in accordance with a schedule of set point temperatures over a control period as a data processor arrangement (10). A signal indicative of the current temperature of the room is received at a temperature input (9) for receiving a signal indicative of the current temperature in the room and a control output (18) for supplying control signals to the system. The controller has at least one electronic memory for storing said schedule of set point temperatures, a relationship, based on known heating or cooling characteristics of the room, between the energy supplied to the system in a portion of the control period and the predicted temperature of the room during that portion and subsequent portions of the control period. The electronic memory also stores a first parameter value representative of the cost of supplying said energy and a second parameter value representative of a predetermined acceptability of variations of the actual or predicted temperature of the room from the set point schedule, wherein the processor arrangement (10) is operable to calculate, for each said portion, the energy to be supplied to the system in order for a plurality of parameter values to satisfy a predetermined criterion, said plurality of parameter values comprising said first parameter value and said second parameter value.