What do you mean by ion product? What is the definition for the ion product of water?

The ion product of water is simply the product of the characteristic cation and anion of water, ##K_w = [OH^-][H^+]##.
The ion product is simply another equilibrium expression. It has been extensively and precisely measured for water at various temperatures, and is most often quoted for standard conditions: 1 atm pressure, 298 K. Under standard conditions, ##K_w = 10^-14##.
Under non-standard conditions, i.e. temperatures greater than 298 K, would you expect ##K_w## to increase or decrease? Why?