Junction temperature is always the key limit. The maximum ambient is worked out from the maximum junction temperature, the power dissipated, and the thermal resistance from junction to ambient.
Suppose the device is dissipating 1W. If the thermal resistance from junction to ambient is 10degC/W, the junction will be 10degC hotter than the ambient, making the maximum ambient 115degcC if the junction has to be kept to 125degC. It is just as simple as this.
If the device were to be dissipating a negligible amount of power, it would be able to run to the full 125degC ambient. You see this expressed as power derating curves against ambient temperature.
The reverse voltage is almost always quite low (and the leakage gets much worse with temperature). But they are great for, say, free wheeling diodes in switching power supplies.