Battery charging voltage

Do you have a diode split charging arrangement in the system? If so, where are you measuring the 'alternator' voltage - at the output of the alternator or the input to the battery?
the alternator is then normally wired for remote sensing of the battery voltage.
alternator wired for remote sensing was my thought as well.
 
Northern Arizona , as you will have already discovered .

BUT if the battery volts rises as it get colder how come a car battery, for example, struggles in cold weather but is fine when its warmer.

A battery does not store electricity. It uses electrical input to drive a chemical reaction on one direction and then it produces electricity by reversing that chemical reaction. All chemical reactions are slower at lower temperatures. Consequently at low temperatures you need a higher voltage to drive charging, and energy delivery on discharge reduces.
Also ohmic resistance rises with lower ttemperature further limiting high rate output but this is a minor effect.
 
Surely the graph is showing the allowable charge voltage at different temperatures, which are higher at low temperatures.

Yes you are right. I have now found a table of OC voltage vs temp. As I expected it rises as the temp rises
 
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