  We address the dephasing dynamics of the quantum Fisher information (QFI) for
the process of quantum thermometry with probes coupled to squeezed thermal
baths via the nondemolition interaction. We also calculate the upper bound for
the parameter estimation and investigate how the optimal estimation is affected
by the initial conditions and decoherence, particularly the squeezing
parameters. Moreover, the feasibility of the optimal measurement of the
temperature is discussed in detail. Then, the results are generalized for
entangled probes and the multi-qubit scenarios for probing the temperature are
analysed. Our results show that the squeezing can decrease the number of
channel uses for optimal thermometry. Comparing different schemes for
multi-qubit estimation, we find that an increase in the number of the qubits,
interacting with the channel, does not necessarily vary the precision of
estimating the temperature. Besides, we discuss the enhancement of the quantum
thermometry using the parallel strategy and starting from the W state.
