I'm afraid that the answer above is confusing kinetic (rate) and thermodynamic (equilibrium) effects.
While temperature does affect both reaction rates and Kc, these are quite separate phenomena. The fundamental reason why Kc depends on temperature is because it is linked to the standard free energy change of reaction through the equation ΔG∘=−RTlnKc. Since ΔG∘ also depends on T, then it follows Kc will depend on T. However, ΔG∘ is mostly independent of pressure and concentration, and so these do not affect the value of Kc.
If pressure is increased, the position of equilibrium may shift according to Le Chatelier's principle to counteract the change, but the ratio of concentrations at equilibrium (i.e., Kc) will remain constant at a given temperature. Similarly, changing the concentration of reactants or products will shift the equilibrium position to maintain the equilibrium constant, but the value of Kc itself does not change since it is a ratio of concentrations at equilibrium and is determined by the inherent properties of the reaction at a specific temperature. While it's true that temperature affects the rates of both the forward and reverse reactions, this is not the reason why Kc changes with temperature.