  We show that certain coherences, termed as heat-exchange coherences, which
contribute to the thermalization process of a quantum probe in a repeated
interactions scheme, can modify the spectral response of the probe system. We
suggest to use the power spectrum as a way to experimentally assess the
apparent temperature of non-thermal atomic clusters carrying such coherences
and also prove that it is useful to measure the corresponding thermalization
time of the probe, assuming some information is provided on the nature of the
bath. We explore this idea in two examples in which the probe is assumed to be
a single-qubit and a single-cavity field mode. Moreover, for the single-qubit
case, we show how it is possible to perform a quantum simulation of resonance
fluorescence using such repeated interactions scheme with clusters carrying
different class of coherences.
