The ionic product of water increases if....

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(D) The auto-ionization of water is an endothermic process: $H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)$.According to Le Chatelier's principle,for

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Temperature is increased

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(D) The auto-ionization of water is an endothermic process: $H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)$.According to Le Chatelier's principle,for an endothermic reaction,an increase in temperature shifts the equilibrium to the right.This results in an increase in the concentration of $H^+$ and $OH^-$ ions.Since the ionic product of water $K_w = [H^+][OH^-]$,an increase in the concentration of these ions leads to an increase in the value of $K_w$.

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