If your always on requirements are very modest, use a Raspberry Pi for that. I mine Curecoin and Foldingcoin with my GPU so my main PC stays running all the time.
This extreme modder got an i3 down to just under 6W at idle.
https://ssj3gohan.tweakblogs.net/blo...-computer.html
Probably not as impressive nowadays since a Tegra X1 might be about on par in terms of CPU, far superior in GPU, and is similarly low power.