*** If there is a moderator around, can they move this post to the Oak Support thread? Thanks ***
The problem here is the Oak/ESP8266 chip can demand bursts of around 200ma from the 3.3v supply, which will increase as the battery voltage drops. So while the battery holder might fit, since a CR2032 is only rated to have somewhere between 190-240mah (down to 2v), unless the battery has uncommonly low internal resistance, the ESP8266 will never get the current it needs, and will thus never properly start. You'd then have the issue of how long will the battery last... you'll be lucky to get 1 hour out of it, and any connected sensors will probably not work at all.
If you don't need the wireless part of the Oak, and just want a high speed micro-controller, you could try shutting down the wireless side of the ESP8266 - it would probably work from a CR2032 then, and would get a couple hours of use from a single battery. However, you'll have better luck using a lithium-ion rechargeable battery on the VIN pins, with some sort of charge management/protection circuitry. Similar to the lipo shield that you could buy for the Oak.
