  We derive exact analytical formulas for the radiative heat transfer between
parallel slabs separated by vacuum and subject to arbitrary temperature
profiles. We show that, depending on the derivatives of the temperature at
points close to the slab--vacuum interfaces, the flux can exhibit one of
several different asymptotic low-distance ($d$) behaviors, obeying either
$1/d^2$, $1/d$, or logarithmic power laws, or approaching a constant. Tailoring
the temperature profile within the slabs could enable unprecedented tunability
over heat exchange, leading for instance to sign-flip transitions (where the
flux reverses sign) at tunable distances. Our results are relevant to the
theoretical description of on-going experiments exploring near-field heat
transfer at nanometric distances, where the coupling between radiative and
conductive heat transfer could be at the origin of temperature gradients.
