Interaction between light and high-frequency sound is a key area in integrated photonics, quantum and nonlinear optics, and quantum science. However, typical suspended optomechanical structures suffer from poor thermal anchoring, making them susceptible to thermal noise arising from optical absorption. Here, we demonstrate a chip-scale, release-free silicon optomechanical crystal cavity operating cryogenically with improved resilience to laser light. Relative to a suspended design, we observe 18 dB suppression of the thermo-optic effect, and the device also sustains near-unity phonon occupation at 35 dB higher intracavity optical energy in continuous-wave operation. Non-exponential decay dynamics from an as yet unidentified thermal process limit transfer of this performance to pulsed operation. Resolving this channel would open a clear path to near-term quantum protocols, such as microwave-to-optical quantum transduction. More broadly, the release-free architecture offers a novel platform for studying thermal noise dynamics with results relevant across silicon optomechanical platforms.