Methods and systems facilitate network communications between a wireless network-connected thermostat and a cloud-based management server in a manner that promotes reduced power usage and extended service life of an energy-storage device of the thermostat, while at the same time accomplishing timely data transfer between the thermostat and the cloud-based management server for suitable and time-appropriate control of an HVAC system. The thermostat further comprises powering circuitry configured to: extract electrical power from one or more HVAC control wires in a manner that does not require a “common” wire; supply electrical power for thermostat operation; recharge the energy-storage device (if needed) using any surplus extracted power; and discharge the energy-storage device to assist in supplying electrical power for thermostat operation during intervals in which the extracted power alone is insufficient for thermostat operation.