  We study the mechanical fluctuations of a micrometer sized silicon cantilever
subjected to a strong heat flow, thus having a highly non-uniform local
temperature. In this non-equilibrium steady state, we show that fluctuations
are equivalent to the thermal noise of a cantilever at equilibrium around room
temperature, while its mean local temperature is several hundred of degrees
higher. Changing the mechanical dissipation by adding a coating to the
cantilever, we recover the expected rise of fluctuations with the mean
temperature. Our work demonstrates that inhomogeneous dissipation mechanisms
can decouple the amplitude of thermal fluctuations from the average
temperature. This property could be useful to understand out-of-equilibrium
fluctuating systems, or to engineer low noise instruments.
