We measured the proton-transfer rate constant from a strong and a weak photoacid to water as a function of temperature. We found that the proton-transfer rate constant for the strong photoacid at high temperatures, T > 300 K, is almost temperature-independent, whereas at low temperatures, T < 300 K, the rate constant exhibits a strong temperature dependence. For the weak photoacid, the rate constant also exhibits a relatively large activation energy in the high-temperature region. Previously, we found that the temperature dependence of the proton-transfer rate constant to alcohols is explained as a continuous transition from nonadiabatic to solvent-controlled limits. The model we used to calculate the proton-transfer rate constant is based on the diffusive propagation of the solvent configuration along a generalized solvent coordinate from the reactant potential surface toward the crossing point with the product potential surface. The proton transfer occurs at the crossing point, and the rate is calculated by a sink term placed at the crossing point. The sink term includes the solvent velocity and the Landau-Zener transmission coefficient. Both the diffusion constant and the Landau-Zener transmission coefficient depend on the dielectric relaxation of the solvent. The calculations are compared with the experimental data and an interpolation expression that bridges the nonadiabatic limit and the solvent-controlled limit.