J.R. S. answered 05/13/19
Ph.D. in Biochemistry--University Professor--Chemistry Tutor
Since presumably you are interested in the solubility of a gas (CO2) in water, the general rules for solubility are different than for solids. The solubility of CO2 in water decreases as the temperature increases. The solubility of CO2 would increase as the pressure increases.
As for the ionization of H2CO3 to 2H+ and CO32-, this would increase with increasing temperature and presumably not be affected by changes in atmospheric pressure.