  We study a flux qubit, made of a superconducting loop interrupted by three
Josephson junctions, which is subject to a temperature gradient. We show that
the heat current induced by the temperature gradient, being sensitive to the
superconducting phase differences at the junctions, depends significantly on
the state of the qubit. We furthermore investigate the impact of the heat
current on the coherence properties of the qubit state. We have found that even
small temperature gradients can lead to dephasing times of the order of
microseconds for the Delft-qubit design.
