  The Bogoliubov quasiparticles move in a practically uniform magnetic field in
the vortex state of high temperature cuprate superconductors. Do the
quasiparticles experience a Lorentz force when set in motion by an externally
applied heat current ${\bf j}_Q$, bending their trajectories and causing the
temperature gradient perpendicular to ${\bf j}_Q$ and the applied field ${\bf
H}$, or is the thermal Hall effect a consequence of Berry phases as in an
intrinsic anomalous Hall effect of a semiconductor/metal with spin-orbit
coupling? Here we show that it is the latter, and for the first time, calculate
the temperature, ${\bf H}$-field and the $d$-wave pairing gap $\Delta$
dependence of the intrinsic thermal Hall conductivity, $\kappa_{xy}$. We find
that the intrinsic contribution to $\kappa_{xy}$ displays a rapid onset with
increasing temperature, which compares favourably with existing experiments at
high ${\bf H}$-fields on the highest purity samples. This finding may help to
settle a much-debated question of the bulk value of the pairing strength in
cuprate superconductors in magnetic field.
