The problem with battery operated RF remote sensors in the fridge and espically in the freezer is .. The batteries tend to not work. (And the frequency may drift)
Beyond that I can not say much.... Now designing a sensor.. It's easier than you think.. inside that Accurite is a small blob known as a thermisistor.. You need to remove it and "remote" it. (Add leads) then route the wires (There is already a path as there's already a thermisistor inside the fridge and a water line into the freezer) and hook the leads back to the sender OUTSIDE where it's warmer.
Alas.... I can not help you there. You will very likely destroy the thermistor (They are cheap but I know not the value> How cheap. oh 10 bucks for half a dozen give or take)
If they are the right value.... Well 3-D printers tend to eat 'em.
