The red battery light comes on when the ambient temp is 35 or higher. It only comes on at 50 mph even if the engine shifts down to a lower gear. It does not come on when the ambient temp is lower than 35. Never seems to affect the running of the engine but I am afraid one day it will and I will be miles from help.I have tried to pin it to a specific RPM but have not been able to. Always on acceleration.
Get yourself a real voltmeter that plugs into the power port. Or for us old guys, the cigarette lighter socket. Watch what it does when the light comes on. The not running battery voltage should be 12.4 or higher.
Start the car and the voltmeter should read 13.8 or so. It can get as high as 14.5 or so. When that light comes on, if the voltage reads battery voltage or about 12 volts your alternator may need replacement. The belt may also be slipping so that should be checked before alternator replacement.
Why does the ambient temperature effect the fact that the light comes on or not?
Check the PCM for fault codes, there are some faults that do not require the check engine light to turn on like battery temperature sensor and ambient temp sensor faults.
Mechanically, there is more friction on a belt that is warm. Electrical current is definitely effected by temperature.