I am not aware of a correlation between heat conductivity (W/K/m) and heat capacity (J/kg/K).
However, I would not exclude some correlation for some groups of materials.
For example, it would be good to go back to the kinetic theory of ideal gases to check for such a link.
In the absence of such a link, we have to be more precise about this question.
For example, we could consider heat conduction in materials with the same heat conductivity.
In that case, the heat capacity delays the propagation of heat waves.
It decreases the overall heat conduction.
This is why, in fire protection, materials with high heat capacity might offer some protection, they retard the propagation.
This effect is summarized in a parameter called heat diffusivity, which is essentially the ratio of heat conductivity and heat capacity.