It does, but the opportunities to observe that are limited, and at a laser (1) Forget heating more, forget attaining the temperature of liquid nitrogen (2) It will be overshadowed by other effects: destruction, end of lasing, other recombinations getting more important, changing effects of doping (3) Already the mean carrier energy in both bands changes faster than the material's gap.
Let's take an example: 10ppm/K expansion, as much on the momentum, hence 20ppm/K on the energy, put signs as you like. For 2eV gap it's 40µV/K drift of the gap. Alone the carriers' thermal energy drifts by 90µV/K. Then, carriers are very far from thermalised in a laser diode, so their mean energy, which defines much the emitted wavelength, depends much on the speed of thermalisation and of recombination.
So while whoever asked the question expects answers like "thermal expansion changes the gap", real life has little to do with it.