Kc is temperature dependent, so changing the temperature will change its value. The type of change depends on whether it's an exothermic or endothermic reaction.
If the reaction is exothermic, increasing the temperature will reduce Kc and vice-verca. This is because if you increase the temp., you drive the equilibrium backwards (in the endothermic direction), and therefore increase the concentration of reactants and decrease the concentration of products.
If endothermic, increasing the temperature will increase Kc, and vice-verca.