  We address the discrimination of structured baths at different temperatures
by dephasing quantum probes. We derive the exact reduced dynamics and evaluate
the minimum error probability achievable by three different kinds of quantum
probes, namely a qubit, a qutrit and a quantum register made of two qubits. Our
results indicate that dephasing quantum probes are useful in discriminating low
values of temperature, and that lower probabilities of error are achieved for
intermediate values of the interaction time. A qutrit probe outperforms a qubit
one in the discrimination task, whereas a register made of two qubits does not
offer any advantage compared to two single qubits used sequentially.
