  Stefan-Boltzmann's law indicates that far-field blackbody radiation scales at
the fourth power of temperature. The temperature dependence of radiative heat
transfer in the near field is expected to be very different due to the
contribution of evanescent waves. In this work, we experimentally observe such
deviation on the radiative thermal conductance by bringing a hot micrometric
sphere in the nearfield of a room-temperature planar substrate, down to a
separation distance of few tens of nanometers. The influence of materials is
assessed by using either SiO2 or graphite spheres, and SiO2, graphite and InSb
substrates. Temperature differences as large as 900 K are imposed. A maximum
near-field radiative thermal conductance of about 70 nW.K-1 is found for a
graphite-graphite configuration. The experimental results demonstrate that the
temperature exponent weakens in the near field, ranging from 2.2 to 4.1,
depending on the gap distance and the materials. These results have broad
consequences, in particular on the design of high-temperature nanoscale
radiative energy devices.
