 
Yes, but in a fairly reproducible way. -40 is only a smidgen of the
distance to absolute zero. And in any case you're going to have to
borrow freezer space from a bio lab or someone to test/calibrate this
darling anyway. Btw, you're probably going to want those big capacitors
you found to fire the solenoid -- High current drain on frozen batteries
can be an ugly thing.