I believe that we're further along than you think.
Renewables currently make up about ⅓ of the world's energy supply, and the percentage is rapidly increasing. If you look at the curve you'll notice that it isn't linear, but is actually increasing exponentially.
That's because of how the cost of fossil fuels continues to increase while the cost of renewable energy continues to decrease, and the rate of conversion is a function of the difference between the two costs per unit energy.
When the cost of renewables becomes less than the cost of fossil fuels, a critical mass will be reached and this will result in an immediate global rush to switch over.
We're very close to that point now, and by 2030, it won't make evonomic sense for most industries to stick with fossil fuels.
By analyzing the data and extrapolating from the predicted future curves, it seems very likely that global CO² output will peak before 2040 and then rapidly decrease in the following decades.
The planet naturally scrubs CO² from the atmosphere and the percentage of CO² will eventually equalize at close to preindustrial levels (they're currently about 50% higher than that).
The rate at which CO² scrubbing takes place isn't well known but it's likely between 25 - 50 years to eliminate about half of the excess.
Assuming all that is true (qualitatively it's true, but the specific timeline is basically an educated guess by climatologists), we should expect global atmospheric temperatures to peak about 1.5 - 2.0 C⁰ above the natural baseline around 2070 - 2080 and then gradually return to normal in the following several decades.
That's certainly cause for concern and it will have an enormous effect on the world's ecosystems, but it's not the absolute catastrophe that so many had been predicting.