Phytoplankton growth depends a lot of the nutrient load and continual fluctuation of those nutrients that 'feed' the community. The two main growth nutrients are nitrogen and phosphorus, but don't forget about the other required macro and micro nutrients. The species composition of phytoplankton changes weekly if not daily due to various influences on the community. There are species that are adapted to thrive in all water temperatures. Nutrient loads and specific nutrient requirements of the species determine the density of algae. Don't expect a die off as water temperatures decrease unless the nutrients significantly decrease or the species encounter a limiting factor. When one most abundant specie dies out due to a limiting factor another specie with slightly different requirements is usually waiting to take its place. Again, total density is usually determined by nutrient availability.