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I was just thinking the same question. I think that the issue with the ESP8266 is the power draw. Although you can Sleep the ESP8266, I have seen posts claiming that there are issues with a stand-alone ESP8266 reconnecting to the DHTxx sensors on Waking. Using the Tiny85 to run Code might alleviate this issue. I would be interested to hear if anyone has any success.
Here are some links to what I have found so far with just using the ESP8266 stand alone on batteries. I am not planning to do any of my own development on this anytime soon so let me know if you get anywhere with running the ESP8266 for extended periods (months) on low power.https://tzapu.com/minimalist-battery-powered-esp82...http://www.bntdumas.com/2015/07/23/how-to-battery-...