We use a general theory of the fluctuating electromagnetic field and a gene
ralized Kirchhoff's law (Ref. 8) to calculate the heat transfer between mac
roscopic and nanoscale bodies of arbitrary shape, dispersive, and absorptiv
e dielectric properties. We study the heat transfer between: (a) two parall
el semi-infinite bodies, (b) a semi-infinite body acid a spherical body, an
d (c) two spherical bodies. We consider the dependence of the heat transfer
on the temperature T, the shape and the separation d, and discuss the role
of nonlocal and retardation effects. We find that for low-resistivity mate
rial the heat transfer is dominated by retardation effects even for the ver
y short separations.