We put a second backup thermostat in our basement for just this reason.
We wired it up so that if the basement drops below 40 or so the furnace
turns on (regardless of how hot it might get upstairs). Not really
ideal, but a few times on really cold nights it has tripped. If I hear
the furnace turn on, and can go adjust the heat vents to put more heat
into the basement. Really I'd like to have some sort of buzzer or
indicator light that alerts me to the fact that the basement is getting
I didn't have handy a thermostat that went that low, actually, so I
just installed a mercury-switch type one at an angle, and subtract 20
from the scale. Tricky to get the angle right, but seems to work.