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Water is a key ingredient for life and plays a central role as solvent inmany biochemical reactions. However, the intrinsically quantum nature of thehydrogen nucleus, revealing itself in a large variety of physicalmanifestations, including proton transfer, gives rise to unexpected phenomenawhose description is still elusive. Here we study, by an unprecedentedcombination of state-of-the-art quantum Monte Carlo methods and path-integralmolecular dynamics, the structure and hydrogen-bond dynamics of the protonatedwater hexamer, the fundamental unit for the hydrated proton. We report aremarkably low thermal expansion of the hydrogen bond from zero temperature upto 300 K, owing to the presence of short-Zundel configurations, characterisedby proton delocalisation and favoured by the synergy of nuclear quantum effectsand thermal activation. The hydrogen bond strength progressively weakens above300 K, when localised Eigen-like configurations become relevant. Our analysis,supported by the instanton statistics of shuttling protons, reveals that thenear-room-temperature range from 250 K to 300 K is a ``sweet spot'' for protontransfer, and thus for many phenomena depending on it, including life.

Thermal dependence of the hydrated proton and optimal proton transfer