The current application is directed to intelligent controllers that continuously, periodically, or intermittently calculate and display the time remaining until a control task is projected to be completed by the intelligent controller. In general, the intelligent controller employs multiple different models for the time behavior of one or more parameters or characteristics within a region or volume affected by one or more devices, systems, or other entities controlled by the intelligent controller. The intelligent controller collects data, over time, from which the models are constructed and uses the models to predict the time remaining until one or more characteristics or parameters of the region or volume reaches one or more specified values as a result of intelligent controller control of one or more devices, systems, or other entities.