  The duality relating the four-dimensional Kerr-Taub-NUT black hole to a
thermal two-dimensional CFT with central charges $c_L=c_R=12 J_0$ is analyzed
in detail, generalizing an argument given recently for Kerr within the
soft-hair approach. The hidden conformal symmetry is realized in the form of
$Vir_L \times Vir_R$ diffeomorphisms which act non-trivially on the black hole
horizon. Semiclassical formulae are derived for the temperature and central
charges of the dual CFT. Assuming the applicability of the Cardy formula, these
CFT quantities precisely reproduce the macroscopic Bekenstein-Hawking area law.
Various further generalizations including the complete family of black holes in
four dimensions are discussed.
