We study spin-lattice relaxation times of electron spins in Er³⁺:CaWO₄ at millikelvin temperature, detected via their coupling to a low-mode volume superconducting resonator. At large magnetic field supporting strong phonon-emission rates, we observe a noticeable increase in relaxation times with increasing spin-excitations, which exhibit a unique [tanh (ℏ ω₀/kB T)]² temperature dependence. These observations are typical of a phonon-bottlenecked spin relaxation, and have implications for quantum technologies that exploit rare-earth spin ensembles as coherent resources.