Heat can be exchanged between two surfaces through emission and absorption of thermal radiation. It has been predicted theoretically that for distances smaller than the peak wavelength of the blackbody spectrum, radiative heat transfer can be increased by the contribution of evanescent waves(1-8). This contribution can be viewed as energy tunnelling through the gap between the surfaces. Although these effects have already been observed(9-14), a detailed quantitative comparison between theory and experiments in the nanometre regime is still lacking. Here, we report an experimental setup that allows measurement of conductance for gaps varying between 30 nm and 2.5 mu m. Our measurements pave the way for the design of submicrometre nanoscale heaters that could be used for heat-assisted magnetic recording or heat-assisted lithography.