The infrared spectrum of hot water observed in a sunspot has been assigned. The high temperature of the sunspot (3200 K) gave rise to a highly congested pure rotational spectrum in the 10-micrometer region that involved energy levels at least halfway to dissociation. Traditional spectroscopy, based on perturbation theory, is inadequate for this problem. Instead, accurate variational solutions of the vibration-rotation Schrödinger equation were used to make assignments, revealing unexpected features, including rotational difference bands and fewer degeneracies than anticipated. These results indicate that a shift away from perturbation theory to first principles calculations is necessary in order to assign spectra of hot polyatomic molecules such as water.