The only thing which can change the value of Kc for a given reaction is a change in temperature. The position of equilibrium, however, can change without a change in the value of Kc. The effect of a change of temperature on a reaction will depend on whether the forward reaction is exothermic or endothermic.

Why does KC change with temperature?

If you increase the temperature, the reaction will shift toward the products in equilibrium, and hence Kc would be have to be changed.

How does KC depend on temperature?

Changes in Temperature

Kc is larger when the reaction shifts right. This occurs if T is increased for an Endothermic Reaction or T is decreased for an Exothermic reaction. Kc is smaller when the reaction shifts left. This occurs if T is decreased for an Endothermic Reaction or T is increased for an Exothermic reaction.