Why not use a smaller Arduino, like a Wemos D1 mini, or even a bare ESP-12.
Power usage is about the same as an Uno, but in a much smaller size.
It's own power use might already keep it warm enough (smaller, same power, so running 'hotter').
Those modules also have plenty of onboard flash (SPIFFS), so the SD card can also go (assuming no video is stored).
With the right (very low drop) regulator, a 3.7volt LiPo should be able to power it for hours.
Smaller also means a smaller enclosure, or thicker insulation. Less heating, smaller battery.
Leo..