Changes:
var url = ‘http://api.thingspeak.com/channels/40743/feed/last.json’;

// Get the angle (convert to radians)
var angle = radians(Number(weather.field1));
// Get the wind speed
var windmag = Number(weather.field1);

I got:
{“created_at”:”2016-04-13T10:52:27Z”,”entry_id”:187950,”field1″:”13″,”field2″:null}

Test conditions were, an ESP-01 board with both LEDs removed and a 330uF cap directly across the board input power pins. Power was supplied by a Tek lab supply and current monitored with 5.5 digit bench DMM. A Lua script was run on power up that connected to the WiFi, connected to an MQTT broker, got the temp from a DS18B20 temp sensor, published the temp, then when into deep sleep for 10sec, & repeat.

Minimum Voltage: At the low end, the device did not reset correctly 100% of the time by about 2.2V, 2.3V seemed stable. Therefore 2.5V should be a pretty safe bet.

Current Consumption: The ESP-01 board with no leds in deep sleep mode consumes about 30uA @ 3.3V. This sounds about right, with the datasheet stating 10uA for the ESP8266, however there is also a flash device on this board fully powered on all the time.

At lower voltages there was no significant reduction in sleep current.

As the voltage increased above about 3.8V there is exponential increase in sleep current

At 4.5V, the sleep current increases to ~2.5mA, or around 100x what it is below 3.8V.

Source: http://forum.makehackvoid.com/t/esp8266-operating-voltage-range-and-sleep-current/286

Source: http://rayshobby.net/first-impression-on-the-esp8266-serial-to-wifi-module/

Building a battery powered WiFi IoT Sensor with ESP8266, MS-5611 (GY-63), nodemcu and MQTT
http://www.agocontrol.com/2015/03/building-a-battery-powered-wifi-iot-sensor-with-esp8266-ms-5611-gy-63-nodemcu-and-mqtt/

While there are a lot of Wifi modules on the market, the ESP8266 has some benefits. It is very cheap, it has a toolchain and powerful firmwares. Together with MQTT and ago control it is very easy to build powerful IoT (buzzword bingo! again) devices.

https://nurdspace.nl/ESP8266
http://bbs.espressif.com/viewtopic.php?f=6&t=133
http://tinker.yeoman.com.au/2015/03/08/reducing-esp8266-power-consumption-using-deep-sleep/
https://hackaday.io/project/3253-esp8266-native/log/11805-nodemcu-firmware
https://github.com/nodemcu/nodemcu-firmware/wiki/nodemcu_api_en#nodedsleep

My temperature meter seems to take average 68 mA from the battery.
No wonder that the batteries run out quickly.
There must be a way to optimize the power consumption.