  We propose an adiabatic method for optimal phonon temperature estimation
using trapped ions which can be operated beyond the Lamb-Dicke regime. The
quantum sensing technique relies on a time-dependent red-sideband transition of
phonon modes, described by the non-linear Jaynes-Cummings model in general. A
unique feature of our sensing technique is that the relevant information of the
phonon thermal distributions can be transferred to the collective spin-degree
of freedom. We show that each of the thermal state probabilities is
adiabatically mapped onto the respective collective spin-excitation
configuration and thus the temperature estimation is carried out simply by
performing a spin-dependent laser fluorescence measurement at the end of the
adiabatic transition. We characterize the temperature uncertainty in terms of
the Fisher information and show that the state projection measurement saturates
the fundamental quantum Cram\'er-Rao bound for quantum oscillator at thermal
equilibrium.
