Collection of sketches for the ESP8285 Development Board available on Tindie for $19.95.
With light sleep mode enabled the average current consumption drops from ~20 mA with modem sleep (default) to around 10 mA at a five second wifi broadcast period. This is small enough that the device can continuously broadcast for more than 24 hours on a small 300 mAH LiPo battery. The current draw is large enough that the temperature reading of the BME280 will typically be a few degrees above the actual ambient air temperature.