  Upon introducing an heavy quark in the perturbative regime of the QCD
conformal window we precisely determine the associated heavy meson spectrum and
wave functions in terms of the number of light flavours and mass. We then
compute the conformal Isgur-Wise function which is a central quantity in heavy
quark physics. We further determine the impact of the residual low energy
confining dynamics on the heavy meson spectrum. As a working framework, we
adapt the heavy quark effective theory to the perturbative conformal window
dynamics. Our work lays the foundations to systematically go beyond the
infinite mass defect approximation in conformal field theories.
