The water hexamer has many low-lying isomers, e.g., ring, book, cage, and prism, shifting from two- to three-dimensional structures. We show that this dimensionality change is accompanied by a drop in the quantum nature of the cluster, as manifested in the red shift of the quantal OH stretching modes as compared with their classical counterparts. We obtain this "nuclear quantum effect" (NQE) as the mean deviation between the OH stretch frequencies from velocity autocorrelation Fourier transforms from classical trajectories on a high-level water potential (MB-pop as compared with scaled harmonic frequencies from high-level quantum chemistry calculations. With a universal scaling factor, the predicted OH frequencies agree with experiment to a mean absolute deviation <= 10 cm(-1), which allows unequivocal isomer assignments. By assuming temperature-independent NQEs, we produce the temperature dependence of the cage isomer OH stretch spectrum below 70 K, where it is the dominant structure. All bands widen and blue-shift with increasing temperature, most conspicuously the reddest mode, which thus constitutes a "vibrational thermometer".