If the blinking red light doesnt go away or keeps coming back a persistent blinking red light can mean a couple of things. Usually your thermostat will take about half an hour to recharge.

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Nest thermostat flashing red light. Youll see a blinking red light at the top of the thermostat display to confirm that its charging. A blinking red light will appear if the nests battery is too low to start. The nest should charge itself within a few hours but you can speed up this process by using a micro usb cable. It should turn back on automatically after the battery is charged. Youll need to check the power readings on your thermostat. Battery is too low to start.
It can take up to an hour if the battery is severely depleted. The nest displays a message that asks you to remove the nest from the base and then reattach it the nests screen is dark or unresponsive you may see a blinking green or red light at the top of the nest the thermostat animations are very slow and unresponsive. Your thermostat has a red blinking light a red blinking light means that the nests battery is running low. This could be due to a wiring problem or extended power outage. You can also speed up the process by disconnecting the thermostat display and plugging it into the usb port that came with your device. But if the battery is fully drained it can take as long as two hours to recharge.
If you dont see a blinking. If your thermostat shows you a blinking red light the battery is charging and it will eventually turn on.