 Solution

GaN has a substantial band-gap advantage for high-temperature operation. Its gap is larger than those of GaAs and GaP, suppressing thermally generated intrinsic carriers through $n_i\propto e^{-E_g/(2kT)}$. A doped junction therefore retains its intended carrier imbalance and can have lower thermally generated leakage over a wider temperature range, other factors being equal. The wide gap also supports emission at higher photon energies.

This is a materials-based expectation, not a guarantee for every finished device. Dopant activation and compensation, defects, contact stability, heat extraction and nonradiative recombination can set the practical limit. Increasing temperature also reduces carrier mobility and can broaden or quench light emission. The relevant advantage is reduced intrinsic excitation; a comparison of operating temperatures needs those other device properties too.