The correct option is A True
Kw is very temperature dependent.
By Le- Chatelier's principle, as the temperature of the system increased, the position of equilibrium position will shift to the right to minimize the effect of the increased temperature.
The forward reaction is favoured reaction resulting in the production of more H+ and OH−, so the value of Kw will increase.
Since the concentration of hydrogen ion is higher at the higher temperature, the pH of water will be lower at higher temperatures.