  We apply estimation theory to a system formed by two interacting trapped
ions. By using the Fisher matrix formalism, we introduce a simple scheme for
estimation of the temperature of the longitudinal vibrational modes of the
ions. We use the ions interaction to effectively infer the temperature of the
individual ions, by optimising the interaction time evolution and by measuring
only over one of the ions. We also investigate the effect of a non-thermal
reservoir over the inference approach. The non-classicality of one of the ions
vibrational modes, introduced due to a squeezed thermal reservoir, improves the
indirect inference of the individual temperatures.
