We analyze the influence of optically generated nonequilibrium phonons on the spin relaxation and effective spin temperature of an individual Cr atom inserted in a quantum dot. Using a three-pulse pump-probe technique, we show that the spin relaxation measured in resonant optical pumping experiments strongly depends on the optical excitation conditions. We observe for an isolated Cr in the dark a heating time shorter than a few hundred nanoseconds after an initial high-power nonresonant excitation pulse. A cooling time larger than a few tens of microseconds, independent of the excitation, is obtained in the same experimental conditions. We show that a tunable spin-lattice coupling dependent on the density of nonequilibrium phonons can explain the observed dynamics. Low-energy excitation conditions are found where the Cr spin states S-z = +/- 1 can be efficiently populated by a nonresonant optical excitation, prepared and read out by resonant optical pumping and conserved in the dark for a few microseconds.