  We study the nonlinear thermoelectric cooling performance of a quantum spin
Hall system. The setup consists of a nanomagnet contacting a Kramers' pair of
helical edge states, resulting in a transmission probability with a rich
structure containing peaks, well-type, and step-type features. We present a
detailed analysis of the impact of all these features on the cooling
performance, based to a large extent on analytical results. We analyze the
cooling power as well as the coefficient of performance of the device. Since
the basic features we study may be present in the transmission function of
other mesoscopic conductors, our conclusions provide useful insights to analyze
the nonlinear thermoelectric behavior of a wide class of quantum devices. The
combination of all these properties define the response of the quantum spin
Hall setup, for which we provide some realistic estimates for the conditions
limiting and optimizing its operation as a cooling device.
