  Large N QCD is mostly governed by planar diagrams and should show linear
confinement when these diagrams are suitably summed. The linear confinement of
quarks in a class of these theories using gravity duals that capture the
logarithmic runnings of the coupling constants in the IR and strongly coupled
asymptotic conformal behavior in the UV was studied in our previous work. We
also extended the theories to high temperatures and argued the possibilities of
meltings and suppressions of heavy quarkonium states. In this paper we give a
formal proof of melting using very generic choices of UV completions, and point
out some subtleties associated with meltings in generic large N theories. Our
proof requires only the existence of well defined UV behaviors that are devoid
of Landau poles and UV divergences of the Wilson loops, allowing degrees of
freedom to increase monotonously with energy scale. We determine the melting
temperatures of heavy quarkonium states, which could suggest the presence of
deconfinement phase transitions in these theories.
