Global Warming and Plat Photosynthesis!?

It has not been determined whether the concentration of CO2 in the atmosphere causes the earth to warm or if a warming earth causes an increased concentration of CO2 in the atmosphere. Anyway, an increase of CO2 in the atmosphere would provide more CO2 for more plants, but I doubt if the availability of CO2 is a limiting factor in plant growth. I would say the growth would be limited either by genetics, uptake of nutrients through the roots, or availability of sunlight.