"...during periods of warming there is more plant activity and more vegetation gives off more of the CO2 gas."

I should probably explain how this could happen, seeing as how vegetation takes in CO2 and gives off oxygen. Vegetation actually does both... when photosynthesis is happening it takes in CO2 and gives off oxygen, when photosynthesis isn't happening (primarily at night) then it takes in oxygen and gives off CO2. When I first learned this I didn't know how there could be more of the CO2 being made... if it's a back and forth process then production of both should ballance out. But an increase of vegetation also means an increase of animal and insect life because of more available food. Animals and insects only take in oxygen and give off CO2, so that's how the ballance tips in favor of an increased level of CO2.