  In a recent Letter [A. Lapolla and A. Godec, Phys. Rev. Lett. 125, 110602
(2020)], thermal relaxation was observed to occur faster from cold to hot
(heating) than from hot to cold (cooling). Here we show that overdamped
diffusion in anharmonic potentials generically exhibits both faster heating and
faster cooling, depending on the initial temperatures and on the potential's
degree of anharmonicity. We draw a relaxation-speed phase diagram that
localises the different behaviours in parameter space. In addition to
faster-heating and faster-cooling regions, we identify a crossover region in
the phase diagram, where heating is initially slower but asymptotically faster
than cooling. The structure of the phase diagram is robust against the
inclusion of a confining, harmonic term in the potential as well as moderate
changes of the measure used to define initially equidistant temperatures.
