My system stops charging the second battery after 10-20 minutes. The main still shows as being charged, but the second battery just shows the current voltage -- 12.4. I am far from proficient in this area, but the second battery seems to draw down without much of a load, leading me to believe that it is not being fully charged even when the NL monitor shows it is fully charged after the 10-20 minutes of charging while driving. Frankly, I have not been satisfied with the system when using my ARB fridge. High heat definitely makes it worse.
I have not torn it a part yet or even fully diagnosed the system. Thanks for any insight you can share.
Try unplugging the controller at the solenoid and leave it that way for a couple days. When you finish your commute or driving around for a bit, leave the engine running and see if the solenoid is still engaged. The aux battery should not stop charging at all unless the main battery has fallen below a certain level. I would also use a volt meter to check level on both batteries when engine is off.
As far as the fridge is concerned, high ambient temperatures will for sure make a difference in how long the JK sized aux battery will last. I purchased the insulated cover for the ARB which helps. The amount of times you go in and out of it, or add warm beverages to it, also makes it work harder.
I think you need to solve your charging issues first though before you get into the fridge efficiency issues as I suspect your aux battery is not getting fully charged. Since we're neighbors if you want to get together and see if we can figure it out, shoot me a pm.