Thermal radiation between parallel objects separated by deep subwavelength distances and subject to large thermal gradients (>100 K) can reach very high magnitudes, while being concentrated on a narrow frequency distribution. These unique characteristics could enable breakthrough technologies for thermal transport control(1-3) and electricity generation(4-8) (for example, by radiating heat exactly at the bandgap frequency of a photovoltaic cell). However, thermal transport in this regime has never been achieved experimentally due to the difficulty of maintaining large thermal gradients over nanometre-scale distances while avoiding other heat transfer mechanisms, namely conduction. Here, we show near-field radiative heat transfer between parallel SiC nanobeams in the deep subwavelength regime. The distance between the beams is controlled by a high-precision micro-electromechanical system (MEMS). We exploit the mechanical stability of nanobeams under high tensile stress to minimize thermal buckling effects, therefore keeping control of the nanometre-scale separation even at large thermal gradients. We achieve an enhancement of heat transfer of almost two orders of magnitude with respect to the far-field limit (corresponding to a 42 nm separation) and show that we can maintain a temperature gradient of 260 K between the cold and hot surfaces at similar to 100 nm distance.