We present linewidth measurements on AlGaAs double heterostructure lasers as a function of temperature and power. The data, which plot observed linewidth as a function of reciprocal power, reveal decreasing slopes and increasing vertical axis intercepts, or power independent linewidths, with falling temperature, consistent with previous experimental observation [D. Welford and A. Mooradian, Appl. Phys. Lett. 40, 560 (1982)]. To explain the power independent linewidth broadening observed in these continuous wave single frequency lasers, we propose that carrier heating processes create a thermal nonequilibrium between electrons and the semiconductor lattice, and that this leads to a power dependent linewidth enhancement factor. From a carrier thermal model we find that the power independent linewidth is mediated by the longitudinal optical (LO)-phonon lifetime (τLO); as τLO is increased (for example, by decreasing the lattice temperature), the noneqilibrium condition is enhanced, and, consequently, the power independent linewidth increases.