  The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the
thermal noise of physical systems in equilibrium. In general however, thermal
equilibrium is an approximation, or cannot be assumed at all. A more general
formulation of the FDT is then needed to describe the behavior of the
fluctuations. In our experiment we study a micro-cantilever brought
out-ofequilibrium by a strong heat flux generated by the absorption of the
light of a laser. While the base is kept at cryogenic temperatures, the tip is
heated up to the melting point, thus creating the highest temperature
difference the system can sustain. We independently estimate the temperature
profile of the cantilever and its mechanical fluctuations, as well as its
dissipation. We then demonstrate how the thermal fluctuations of all the
observed degrees of freedom, though increasing with the heat flux, are much
lower than what is expected from the average temperature of the system. We
interpret these results thanks to a minimal extension of the FDT: this dearth
of thermal noise arises from a dissipation shared between clamping losses and
distributed damping.
