We use the general theory of the fluctuating electromagnetic field and a ge
neralised Kirchhoff's law [8] to calculate the heat transfer and vacuum fri
ction between macroscopic and nanoscale bodies of arbitrary shape, dispersi
ve and absorptive dielectric properties. We study the heat transfer and vac
uum friction between: (a) two parallel semi-infinite bodies, (b) a semi,inf
inite body and a spherical body. We consider the dependence of the heat tra
nsfer and vacuum friction on the temperature T, the shape and separation d,
and discuss the role of non-local and retardation effects. We find that fo
r low-resistivity material the heat transfer and vacuum friction are Domina
ted by retardation effects even for the very short separations.