I would go with this image here http://forum.banana-pi.org/t/bpi-m3-new-image-bpi-m3-ubuntu-16-04-beta-mate/1440/18?u=tkaiser (not the featured one in the thread but the hybrid I created). Read throught the thread to get an idea how/what to fix afterwards (kernel updates for example -- 'Team BPi' still only provides a brain-dead way to apply these fixes but it's wort the efforts).
And you should install a RPi-Monitor to get a clue what's going on. Installer available as well as description what to expect. Common problem is not heat (since throttling works) but most likely undervoltage/undercurrent: http://linux-sunxi.org/Banana_Pi_M3#Sudden_shut_offs_.2F_maximum_consumption_.2F_cooling_vs._consumption