  We study the time-dependent transport of heat in a nanoscale thermal switch.
The switch consists of left and right leads that are initially uncoupled.
During switch-on the coupling between the leads is abruptly turned on. We use
the nonequilibrium Green's function formalism and numerically solve the
constructed Dyson equation to determine the nonperturbative heat current. At
the transient regime we find that the current initially flows simultaneously
into both of the leads and then afterwards oscillates between flowing into and
out of the leads. At later times the oscillations decay away and the current
settles into flowing from the hotter to the colder lead. We find the transient
behavior to be influenced by the extra energy added during switch-on. Such a
transient behavior also exists even when there is no temperature difference
between the leads. The current at the long-time limit approaches the
steady-state value independently calculated from the Landauer formula.
