The temperature dependence of the equilibrium constant is given by the van't Hoff equation: d(ln K)/dT = \Delta H° / RT^2. For an endothermic reaction, \Delta H° > 0, so d(ln K)/dT > 0, meaning K increases as temperature increases. Raising temperature for an endothermic reaction provides the energy needed to drive the forward reaction further, shifting equilibrium to the right and increasing the ratio of products to reactants at the new equilibrium, which means K_c increases. Option A is incorrect reasoning: while Le Chatelier's principle says the system opposes the temperature rise by absorbing heat, this means the endothermic forward reaction is favoured, which increases K_c — not decreases it. Option C is fundamentally wrong; K_c is temperature-dependent and changes with temperature, unlike rate constants which change differently. Option D is the opposite of reality for endothermic reactions; K_c increases with temperature for endothermic reactions and decreases for exothermic ones. This van't Hoff relationship is a critical NCERT thermodynamic concept linking \Delta G° = -RT ln K to temperature. Plausibility check: at higher temperature, the new K_c > 2.0 \times 10^{-3} for an endothermic process, consistent with our conclusion.