Wyze Thermostat Clicking and no screen

Are you measuring voltage while it is attempting to power up, or open circuit voltage? As
I said earlier, you should try to hook the thermostat up as close to the furnace as possible to determine if it is a problem with the wiring or a problem with the thermostat. If the thermostat keeps resetting when hooked up to the furnace at the splice point, then you should contact wyze and get a replacement. If it works properly there, then the next step is finding all bad connections in the wiring- you may need a tech for this.

Just having sufficient voltage available when nothing is hooked up to it is not enough, it also needs enough current availability that the voltage won’t drop below the operational threshold as soon as a load is applied.

Agreed.

I had a power outage last night and my thermostat has been clicking since the power came back on. It was working fine before. Now it clicks and won’t turn on. The outside temp is a balmy 15 degrees with a wind chill of -4. I have small children and am in need of assistance. We have been without heat for 10 hours now.

hopefully you already figured this out, but you can bridge R and W to force the heat on.