Near-field heat transfer between two closely spaced media can exceed in orders radiation through the interface of a single black body. This effect is caused by exponentially decaying (evanescent) waves, which form the photon tunnel between two transparent boundaries or boundaries supporting surface waves. However, in the infrared range this huge energy transfer holds only in the case when the gap between two media is as small as a few tens of nanometers. We propose a different paradigm of the radiation heat transfer, which makes possible the strong photon tunneling (and therefore giant radiative heat transfer) for micron-thick gaps. For it the air gap between two media should be modified, so that evanescent waves are transformed inside it into propagating ones. This modification is possible without increasing the phonon thermal conductance between two media. The suggested structure containing arrays of nanotubes or nanowires is designed so that the photovoltaic conversion of the transferred heat will not be altered by these arrays.