In accordance with the teachings of the commonly assigned U.S. Ser. No. 13/269,501, the commonly assigned U.S. Ser. No. 13/275,307, and others of the commonly assigned incorporated applications, the smart thermostat 102 (FIG. 1) represents an advanced, multi-sensing, microprocessor-controlled intelligent or “l(fā)earning” thermostat that provides a rich combination of processing capabilities, intuitive and visually pleasing user interfaces, network connectivity, and energy-saving capabilities (including the presently described auto-away/auto-arrival algorithms) while at the same time not requiring a so-called “C-wire” from the HVAC system or line power from a household wall plug. In some instances, such advanced functionalities can require a greater instantaneous power draw than a “power-stealing” option (i.e., extracting smaller amounts of electrical power from one or more HVAC call relays) can safely provide. By way of example, in some circumstances, the head unit microprocessor 1102 draws on the order of 250 mW when awake and processing, and an LCD module (not shown) draws on the order of 250 mW when active. Moreover, the Wi-Fi module 1112 draws 250 mW when active, and needs to be active on a consistent basis such as at a consistent 2% duty cycle in common scenarios. However, in order to avoid falsely tripping the HVAC relays for a large number of commercially used HVAC systems, power-stealing circuitry is often limited to power providing capacities on the order of 100 mW-200 mW, which would not be enough to supply the needed power for many common scenarios.