You are correct in thinking that the solubility of a gas will decrease when the pressure over the solution is decreased but the solubility of a dissolved gas will decrease when the solution is heated. This sounds backwards since we usually heat up a solvent in order to dissolve something. The overall energy of a system is dependent on enthalpy and entropy. Temperature is associated with entropy or randomness. If you heat up a solution of a gas and the gas escapes, the system becomes more random therefore it is favorable to have a decrease in solubility.

This relationship is easy to remember if you think about what happens when you open a container of pop. The carbon dioxide bubbles out of the solution...at times, faster than we want it to...if the container is warm.