  Coherent quantum oscillators are basic physical systems both in quantum
statistical physics and quantum thermodynamics. Their realizations in lab often
involve solid-state devices sensitive to changes in ambient temperature. We
represent states of the solid-state optomechanical oscillator with
temperature-dependent frequency by equivalent states of the mechanical
oscillator with temperature-dependent energy levels. We interpret the
temperature dependence as a consequence of strong coupling between the
oscillator and the heat bath. We explore parameter regimes corresponding to
anomalous behavior of mechanical and thermodynamic characteristics as a
consequence of the strong coupling: (i) The localization and the purification
induced by heating, and (ii) the negativity of two generalized heat capacities.
The capacities can be used to witness non-linearity in the temperature
dependency of the energy levels. Our phenomenological experimentally-oriented
approach can stimulate development of new optomechanical and thermomechanical
experiments exploring basic concepts of strong coupling thermodynamics.
