As John correctly points out the solubility of CO2 in water decreases as the temperature increases - making it less soluble and causing the CO2 to outgas more easily... This, among other things, is generally believed to cause global warming, as the oceans temperature are rising causing more CO2 in the atmosphere and more increase in temperature - a vicious cycle.
However, the effect in our aquariums would be fairly small going from say 26 to 23 degrees, but by lowering the temp your lowering the metabolism of the plants and increase bio-available CO2 which is a win-win for your tank - your natural equilibrium in a non-injected tank will be around 3 ppm. which is not worth worrying about testing for.
Cheers,
Michael