  Distinguishing hot from cold is the most primitive form of thermometry. Here
we consider how well this task can be performed using a single qubit to
distinguish between two different temperatures of a bosonic bath. In this
simple setting, we find that letting the qubit equilibrate with the bath is not
optimal, and depending on the interaction time it may be advantageous for the
qubit to start in a state with some quantum coherence. We also briefly consider
the case that the qubit is initially entangled with a second qubit that is not
put into contact with the bath, and show that entanglement allows for even
better thermometry.
