If you want to do a project with wireless communication and don’t mind writing the communications software at a low level (or want to learn how to do this) check out the development system from TI. Note: this is much less capable than something like wifi, but much lower power (both Watts and processing power).
Some background information about battery choices for energy harvesting applications.
Using energy harvesting techniques to get energy from insects to power onboard sensors/controls. http://t.co/9Mn2ZrGL
Many energy harvesting sources generate very low voltage and/or current. The link below is for a TI product that boosts the voltage to useful levels.