  This paper reports on an experimental study of the contact resistance of Hall
bars in the Quantum Hall Effect regime while increasing the current through the
sample. These measurements involve also the longitudinal resistance and they
have been always performed before the breakdown of the Quantum Hall Effect. Our
investigations are restricted to the $i=2$ plateau which is used in all
metrological measurements of the von Klitzing constant $R_K$. A particular care
has been taken concerning the configuration of the measurement. Four
configurations were used for each Hall bar by reversing the current and the
magnetic field polarities. Several samples with different width have been
studied and we observed that the critical current for the contact resistance
increases with the width of the Hall bar as previously observed for the
critical current of the longitudinal resistance. The critical currents exhibit
either a linear or a sublinear increase. All our observations are interpreted
in the current understanding of the Quantum hall effect brekdown. Our analysis
suggests that a heated region appears at the current contact, develops and then
extends in the whole sample while increasing the current. Consequently, we
propose to use the contact resistance as an electronic thermometer for the Hall
fluid.
