[RWebb]

for your appl. use a stirred ice bath to check or calibrate

the thermocouple connected to a Fluke multimeter will be a Type K - not the best for this range, but should be ok for your use. I use a type T Tcple for this range, but they are specialized.

one "error" you are getting is the fact that you are measuring the local T of any pool of air that the Tcple sits in - i.e. all the air will not be well mixed

set a pot of water in there and stick the Tcpl in that - check it the next day; make up a little graph above, at, and below the T you want to measure with at least 3 points on it - Fridge readout vs. the Tcple (you did check the Tcple in the ice bath, right?)

I wouldn't trust the fridge readout much