It’s basic Chemistry 101. Look up the Ksp of CO2 in water. As temperatures increase, CO2 is released. If you’re not a chemist and don’t have a CRC manual handy, then open 2 soda cans (one hot and one cold) and see the difference in CO2 solubility/release from water.
As it gets warmer, CO2 is less soluble in water and thus is released.
By the way, research is not “wrong” but it’s useless when the dataset is wrong. Ice core, sediment core, tree ring, peat bog, etc, are not thermometers. Using them is “a guess” at best and a source of manipulation at worst.