Solubility of carbon dioxide in water under various conditions

re. Le Chatelier's Principle

CO2(g)+H2O(l) ⇌ H2CO3(aq) (∆H<0)

As temperature increases, generally the solubility of solids and liquids increases, while the solubility of gases decreases. Hence the solubility of CO2 decreases as temperature increases, moving the equilibrium to the left. Additionally, the forward reaction is exothermic, so heat is liberated as the reaction proceeds from left to right, and conversely heat is absorbed as it goes right to left.

If the partial pressure of CO2 is increased [eg pumping more CO2into the vessel], the reaction will move to the right so some of the added CO2 goes into solution.
If the total pressure is increased, [eg pushing a plunger into the vessel], the equilibrium will move to the right to partly reduce the increased pressure, ie by dissolving some of the gaseous CO2.