A:Answer This sound like a battery issue (common for these). #1 - do you have 5 wires hooked up or 4 (C wire or no)? #2 - if your heat (assuming based on context) is constantly running to keep up with your request to hit 71, you are not getting power to the Nest. It is all being used by your furnace. Potential solutions - get a pro to add a C wire, use a C wire adaptor (produced by Google), or allow your Nest to come down from 71 naturally for a couple hours while you charge it, then remount it when you go to bed to kick heat back on say an hour or two before you wake up.
