An isosbestic point in the temperature dependence of an absorption spectrum is commonly viewed as a sign of interconverting chemical or structural species. Here I explore an alternative microscopic origin of temperature-independent absorbance in inhomogeneously broadened spectra: While the equilibrium probability of observing a particular frequency generally changes with the magnitude of thermal fluctuations, the weight of at least one frequency is insensitive to small changes in temperature. The range of temperature accessible to aqueous solutions at ambient pressure is sufficiently small that such insensitivity would appear in experiments as an isosbestic point. This mechanism depends only on the continuity of equilibrium distributions, not on the presence of multiple components. Even the simplest model of a single solute species in a fluctuating environment exhibits isosbestic points, van't Hoff behavior, and, with appropriate dependence of transition frequency on configuration, multiple absorption peaks.