Heat travels in solids thanks to phonons. In clean non-magnetic crystalline insulators, thermal conductivity is governed by Umklapp phonon-phonon collisions and phonons become ballistic at cryogenic temperatures. The thermal conductivity peaks at an intermediate temperature where most phonon-phonon collisions cannot produce entropy. Recently, a phonon thermal Hall signal has been observed in numerous insulators. In all cases, the thermal Hall angle is maximum at this peak temperature, and its maximum amplitude does not exceed an intriguing upper bound independent of the phonon mean-free-path. I will argue that a plausible explanation of this experimental observation is to be found beyond the adiabatic and the harmonic approximations. Combined with anharmonicity, the breakdown of the Born-Oppenheimer approximation in a magnetic field can offer a geometric phase to acoustic phonons. The expected bound to thermal Hall angle is close to what is seen experimentally in black P, Ge and Si.