Funny that I buy those exact same LiPos for my quadcopters, and never considered using them for an ESP8266. How much time do you get out of those if you're using a DHT22 sensor?

Funny enough, a battery-powered DHT22 is my next project, so I don’t know yet! But in my other experience the expensive part is powering on the radio, which spikes to 200-300mA at startup and then will sustain around 80mA as long as it’s on.

Well, I'm running a test with 2xAA batteries. With a modified version of https://github.com/rcarmo/azure-iot-esp-01-minimal-cpp that only wakes up every 15m to send a single multicast packet and the power LED removed, the battery's still at 3.08V after two months :)