Laser Diodes to work it in high temperature
Several things:

The power of a laser diode may be limited by the light intensity causing damage to the facets, independently of the thermal effects.  The datasheet should tell you both the maximum instantaneous (optically limited) power and the maximum average (thermally limited) power.

Attempting to run more current through the diode may not be effective because at a certain point you may run out of charge carriers.  At higher voltages the charge carriers may also be pulled out of the active region so they are not in a good location to lase.  (I am guessing here.)

Also, if your device is not designed to operate at high temperatures, it may not act properly due to the number of holes and electrons popped out of the Fermi sea by thermal effects: the free carriers act metalish instead of semiconductorish and just conduct without providing any light.  Even at more conventional temperatures, laser diode efficiency drops significantly just going from 20C to 50C.