  We studied the thermal conduction through a quantum point contact (QPC),
defined in GaAs-AlGaAs heterostructure, in the presence of a transverse
magnetic field. A shift in the position of thermo-voltage peak is observed with
increasing field. The position of the thermo-voltage peak follows the
Cutler-Mott relation in the small field regime (B < 0.5 T); it starts diverging
from the Cutler-Mott relation in the moderate field regime, where a cubic
magnetic field term dominates over the trivial quadratic term; eventually the
shift saturates in the large field regime (B > 3.0 T). Our results suggest that
additional calibration is necessary when using QPC as thermometry, especially
when the transverse magnetic field is applied.
