  We introduce the estimation protocol for detecting the temperature of the
transverse vibrational modes of linear ion crystal. We show that thanks to the
laser induced laser coupling between the vibrational modes and the collective
spin states the estimation of the temperature is carried out by set of
measurements of the spin populations. We show that temperature estimation
protocol using single ion as a quantum probe is optimal in a sense that the set
of state projective measurement saturates the fundamental Cramer-Rao bound. We
find a plateau of the maximal temperature sensitivity using ion chain as a
quantum probe. Moreover, we show that the non-classical part of the quantum
Fisher information could leads to enhancement of the temperature sensitivity
compared to the single ion case.
