So did some quick tests of a power supply circuit. For a while I was thinking of more complex circuits, but have settled on using a diode bridge into a cap with an OKI-78SR switching regulator that outputs 5V and can tolerate up to 36V input. I hooked that 5V through a resistor to a LiPoly battery. This is A TEST CASE, and NOT a suggestion. You can NOT trickle charge LiPoly batteries.
The final circuit will look at the battery voltage and turn off charging when voltage on the battery hits 4.2V.
The ARMstamp can do that, but a simple comparator might be a more prudent choice. With this arrangement I think I can charge the battery with a 100 mA charging circuit.
Here is my bench test.
Post details of your projects here.
After the experiments, I have a very preliminary schematic for the Web enabled thermostat. Still need to connect the dots, and add some bypass caps. Should be doing a layout this week.