  We analyse the impact of temperature on the diffusion coefficient of an
inertial Brownian particle moving in a symmetric periodic potential and driven
by a symmetric time-periodic force. Recent studies have revealed the low
friction regime in which the diffusion coefficient shows giant damped
quasi-periodic oscillations as a function of the amplitude of the time-periodic
force [I. G. Marchenko et al., Chaos 32, 113106 (2022)]. We find out that when
temperature grows the diffusion coefficient increases at its minima, however,
it decreases at the maxima within a finite temperature window. This curious
behavior is explained in terms of the deterministic dynamics perturbed by
thermal fluctuations and mean residence time of the particle in the locked and
running trajectories. We demonstrate that temperature dependence of the
diffusion coefficient can be accurately reconstructed from the stationary
probability to occupy the running trajectories.
