Noninvasive in-situ monitoring of viscoelastic characteristics of corneal tissue at elevated temperatures are pivotal for mechanical property-informed refractive surgery techniques, including thermokeratoplasty and photorefractive keratectomy, requiring precise thermal modifications of the corneal structure during these surgical procedures. This study harnesses Brillouin light scattering spectroscopy as a biosensing platform to non-invasively probe the viscoelastic properties of ovine corneas across a temperature range of 25 - 70°C. By submerging the tissue samples in silicone oil, consistent hydration is maintained, allowing for their accurate sensing of temperature-dependent mechanical behaviors. We identify significant phase transitions in the corneal tissue, particularly beyond 40°C, likely due to collagen unfolding, marking the beginning of thermal destabilization. A subsequent transition, observed beyond 60°C, correlates with collagen denaturation. These phase transformations highlight the cornea's sensitivity to both physiologically reversible and irreversible viscoelastic changes induced by mild to high temperatures. Our findings underscore the potential of Brillouin biosensing technique for real-time diagnostics of corneal biomechanics during refractive surgeries to attain optimized therapeutic outcomes.