  We study the backaction of quantum measurements on heat transport through a
two-level system by considering the continuous quantum measurement onto an
eigenstate of the two-level system. For the nonselective measurement, the
backaction appears as a dephasing effect on the two-level system. We formulate
the heat current under the selective measurement with a stochastic master
equation and show that the cross-correlation between the measurement outcomes
and the heat current contains information on the backaction. We expect that our
findings can be verified by using a platform of superconducting circuits.
