  We consider a model for an edge state of electronic systems in the quantum
Hall regime with filling $\nu=1$ and in the quantum spin Hall regime. In both
cases the system is in contact with two reservoirs by tunneling at point
contacts. Both systems are locally driven by applying an ac voltage in one of
the contacts. By weakly coupling them to a third reservoir, the transport of
the generated heat is studied in two different ways: i) when the third
reservoir acts as a thermometer the local temperature is sensed, and ii) when
the third reservoir acts as a voltage probe the time-dependent local voltage is
sensed. Our results indicate a chiral propagation of the heat along the edge in
the quantum Hall case and in the quantum spin Hall case (if the injected
electrons are spin polarized). We also show that a similar picture is obtained
if instead of heating by ac driving the system is put in contact to a
stationary reservoir at a higher temperature. In both cases the temperature
profile shows that the electrons along the edge thermalize with the closest
"upstream" reservoir.
