In he summer, I don’t leave my phone in direct sunlight for extended periods or else it will overheat. Simply placing it in the shade or in a pocket prevents this. It usually only hits 100 here, so I don’t have experience with the 100-120F range and overheating.
Tl;dr Prevent your phone from reaching extreme temperatures and it will work fine.
It’s just battery chemistry, current capacity and voltage are depressed by low temps.
Some phones aren’t engineered very well and regularly pull current near their battery’s capacity which is just poor design.
It's possible that the phone generated enough heat to stay warmer though. The main problem with operating it was actually how cold my hand that's holding the phone gets since it doesn't move like the other hand does. I had to wear double gloves.