How are Operating Temperature Bands Determined?
All those Temperature Ranges are standards. Some defined by some authority, some just common consent. For example AEC-Q100 is the temperature range you have to expect in the internals (not motor room!) of a car. In Winter of Northern Countries you may have temperatures as low as -40°C. Your Car has to work without problems there. 105°C apply to a Car parked in a hot area in direct sunlight.

I expect that the 125°C max in many applications is also determined by material. 125°C is the maximum allowed temperature for most semiconductors.