Re: tempature adjustment on conductors
The first thing you need to consider is total conductor ampacity. See 310.15(A)(2) and the exception. Basically, this means if the conductors originate and terminate within the same ambient temperatue, than the abient temperature can be used for the calculation. However, if a transition is made from another location into this location, the lowest allowed ampacity will have to be used for the entire circuit based on the higher temperature outside the cooler area.
If the transition is less than 10' or 10% of the circuit (lower of the two) the higher ampacity can be used.
This is usually for considerations into higher ambient temperatures. I this case, no deration would be required for the area within the cooler. Even though the conductor will easily be able to handle ampacities above Table 310.16, which is based on 86 degrees, I would not exceed the values shown in this table or for those values in 240.4(D)
You may want to consider engineering assistance considering there may be other factors and things to consider in such a low temperature that the code does not specify. My first concern would be insulation integrity and conductor brittleness.