  We present a quantum thermometry method utilizing an optomechanical system
composed of an optical field coupled to a mechanical resonator for measuring
the unknown temperature of a thermal bath. To achieve this, we connect a
thermal bath to the mechanical resonator and perform measurements on the
optical field, serving as a probe thermometer. Using the open quantum systems
approach, we numerically calculate the quantum Fisher information for the
probe. We find that, in specific parameter regimes, the system exhibits
clusters of densely packed energy eigenstates interspaced with substantial
energy gaps. This clustering of energy levels results in quasi-degeneracy
within these energy eigenstate groups and hence widens the operational range of
temperature estimation. Moreover, thermal sensitivity, especially at low
temperatures, can be further boosted by appropriately tuning the essential
system parameters.
