There might be some projections that don't take this into account (though I'm not aware of any). However, many consider "commitment", or the long term effects of what has already been done (for example, the CO₂ that's already been produced). I found the following article "What would happen to the climate if we stopped emitting greenhouse gases today?"[0] from 2014 useful in describing the situation with links to additional resources:

[0]: https://theconversation.com/what-would-happen-to-the-climate...

For two examples of projections taking the effects of differences in CO₂ emissions (which serve as an effective proxy for fossil fuel usage), here are two from resources linked from that article:

Charts showing different projections of relative CO₂ concentrations based on varying changes in CO₂ emissions[1]

[1]: http://www.ipcc.ch/publications_and_data/ar4/wg1/en/faq-10-3...

Two global coupled climate models show that even if the concentrations of greenhouse gases in the atmosphere had been stabilized in the year 2000, we are already committed to further global warming of about another half degree and an additional 320% sea level rise caused by thermal expansion by the end of the 21st century.[2]

[2]: http://science.sciencemag.org/content/307/5716/1769

Speeding up the transition to renewable carbon based fuel production would be more than sufficient.

Do you have references which support this claim? I'd be interested in reading about them if you do. Statements like this seem to sometimes be based on the assumption that market forces will be able to fix climate change issues, though I don't know whether you hold this position. The relationship between market forces and effects on climate change are not tightly coupled. The rate at which renewable energy sources replace fossil fuels is not directly proportional (inversely or otherwise) to atmospheric CO₂ concentration or global albedo or temperature or sea level.

From what we understand of human psychology, we don't intuitively grasp concepts on such a grossly non-human scale (both in time and space) such as climate change, just as quantum mechanics or relativistic physics can throw us for a loop. I should think it's much more difficult for the market as a whole to be efficient in reacting to effects on this scale as they are so much further removed from human intuition.