  Statistical physics in equilibrium grants us one of its most powerful tools:
the equipartition principle. It states that the degrees of freedom of a
mechanical system act as a thermometer: temperature is equal to the mean
variance of their oscillations divided by their stiffness. However, when a
non-equilibrium state is considered, this principle is no longer valid. In our
experiment, we study the fluctuations of a micro-cantilever subject to a strong
heat flow, which creates a highly non-uniform local temperature. We measure
independently the temperature profile of the object and the temperature yielded
from the mechanical thermometers, thus testing the validity of the
equipartition principle out of equilibrium. We demonstrate how the fluctuations
of the most energetic degrees of freedom are equivalent to the temperature at
the base of the cantilever, even when the average temperature is several
hundreds of degrees higher. We then present a model based on the localised
mechanical dissipation in the system to account for our results, which
correspond to mechanical losses localised at the clamping position.
