It is likely that the amount of photosynthetic plytoplankton will great increase due to an increase in global temperatures.
An increase in temperature generally increases the rate of chemical reactions including those involved in photosynthesis. In cold climates the action of photosynthetic bacteria stops when the temperature drops below freezing and slows down greatly at lower temperature.
During the Mezozoic Era there is fossil evidence that the temperatures were significantly warmer than present temperatures. This was the time that lush forest produced the vast coal beds, that are mined for energy today. The energy stored in the coal came from photosynthesis.
An increase in temperature will most likely result in an increase in photosynthesis.