Ah ha, that's good to know! Yeah in my case I had a small solar panel (a few quid of eBay, I guess around 1W) which was able to power it through a British winter (it did get direct sunlight though). I had some rechargable AAA batteries and just wired the solar panel in parallel with them.

After a few months it stopped working, I think some moisture got in and the DHT11 failed.