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How does the temperature affect the solubility of CO2 in water?

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Generally, gasses are less soluble in water at higher temperatures. This is govern by the partial pressure that the gas in the liquid (in this case, water) exerts. We can simply say that as the temperature is increased, movements increase (due to kinetic effects) thus the rate of escaping of the gas molecules in the atmosphere increase. The result will be lesser moles of gas dissolved in the solvent (water).

To illustrate this kind of relationship, we can shot it in the form of experiments. One example of it would be the reaction of aqueous CO2 with sodium hydroxide to form Sodium carbonate. The reaction will be as follows:
CO2(aq) + NaOH(aq) → NaHCO3(aq)
Soda water contains dissolved CO2 that can react with NaOH. Different temperature of soda water contains different amount of CO2 dissolved in it so the NaOH needed will also vary. 
As the temperature of the water with CO2 increase, lesser amount of NaOH is needed to form NaHCO3. 

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