The primary negative feedback loop is increased photosynthesis. As CO2 concentrations rise, there's more carbon in the air that can support plant life. There also tends to be both more sunlight (warmer air can support more water vapor before it precipitates into clouds) and more water (in absolute terms, from increased evaporation).
Note that in the near term, the negative feedback of photosynthesis may be overwhelmed by changes in ecosystems: if the climate changes rapidly, whole forests may find themselves in a different biome, ocean circulation patterns may change, more freshwater may enter estuaries, etc. Plants evolve quickly, though, and most of their carbon sequestration is through algae and seaweed with short lifespans.
Unfortunately, I think human land use is impeding that feedback mechanism, as there are large portions of land area that are not allowed to freely green up anymore.
That'll change as human-caused global warming results in widespread crop failures and migration of people. We're at the top of the food pyramid; change an ecosystem and (most of) humanity is the first to go. It only takes about one human generation for an ecosystem to recover after humans leave: Chernobyl and the Korean DMZ are among the most pristine environments on earth now.
This is probably cold comfort for the billions of people that will die.
Note that in the near term, the negative feedback of photosynthesis may be overwhelmed by changes in ecosystems: if the climate changes rapidly, whole forests may find themselves in a different biome, ocean circulation patterns may change, more freshwater may enter estuaries, etc. Plants evolve quickly, though, and most of their carbon sequestration is through algae and seaweed with short lifespans.