  Heat transport in the quantum Hall regime is investigated using micron-scale
heaters and thermometers positioned along the edge of a millimeter-scale two
dimensional electron system (2DES). The heaters rely on localized current
injection into the 2DES, while the thermometers are based on the thermoelectric
effect. In the $\nu = 1$ integer quantized Hall state, a thermoelectric signal
appears at an edge thermometer only when it is "downstream," in the sense of
electronic edge transport, from the heater. When the distance between the
heater and the thermometer is increased, the thermoelectric signal is reduced,
showing that the electrons cool as they propagate along the edge.
