pH change with temperature
The pH of a solution is dependent on acid/base equilibria of the substances in the solution. Each of these equilibria will be affected differently by temperature changes. If reactions are endothermic, the equilibrium will shift towards the products upon increasing temperature, otherwise towards the reactants. How much the equilibrium shifts depends on how exo/endothermic the reaction is.

One of the equilibria is the autodissociation of water, which is endothermic. Increasing the temperature will increase product (H+ and OH-) concentration in pure water. Per definition, the pH will decrease as the H+ concentration (or activity) increases.

More complex solutions will either show an increase or a decrease in pH when temperature is raised. For example, some buffers are notorious for changing pH a lot while others are pretty stable, see this table.