Non-uniformity of temperatures appears as a general rule in hot nanofiber synthesis reactors, where local variations of the balance between long-range radiative heat exchanges and short-range conductive heat exchanges are driven by size and composition of structures. Metal particles larger than a few tens of nanometer are radiation captors, when fiber bodies thinner than 10 nm are transparent. We note that typical gradient lengths correspond remarkably well to usual length of nanotubes (micron range), and increase with fiber radius. For anisotropically radiating reactors as well as for furnace-type reactors, difference between radiative and conductive environments allows temperature intervals as high as several hundred degrees. Practically, axial thermal gradients arise by fiber attachment to a metallic particle, eventually at each tip (ideally with different sizes or compositions), or by attachment to a hot wall (electrode, supporting substrate, or target). The resulting thermal gradients are unusually stiff, typically 10 Kmm-1. We show that local temperature evolution in early stage of nucleation is triggered by dimension of attached particle(s). We show that a diffusion flux of adatoms induced by the axial thermal gradient is quantitatively consistent with a feeding flux, as measured for different reactors. In addition, we notice that the spontaneous minimization of free energy at fiber tip is such that a temperature drop favors axial extension.