  Water is a key ingredient for life and plays a central role as solvent in
many biochemical reactions. However, the intrinsically quantum nature of the
hydrogen nucleus, revealing itself in a large variety of physical
manifestations, including proton transfer, gives rise to unexpected phenomena
whose description is still elusive. Here we study, by an unprecedented
combination of state-of-the-art quantum Monte Carlo methods and path-integral
molecular dynamics, the structure and hydrogen-bond dynamics of the protonated
water hexamer, the fundamental unit for the hydrated proton. We report a
remarkably low thermal expansion of the hydrogen bond from zero temperature up
to 300 K, owing to the presence of short-Zundel configurations, characterised
by proton delocalisation and favoured by the synergy of nuclear quantum effects
and thermal activation. The hydrogen bond strength progressively weakens above
300 K, when localised Eigen-like configurations become relevant. Our analysis,
supported by the instanton statistics of shuttling protons, reveals that the
near-room-temperature range from 250 K to 300 K is a ``sweet spot'' for proton
transfer, and thus for many phenomena depending on it, including life.
