Sorry to intrude again!
I ran the equation a few times.
The equation is written in short:
Energy = 390 + 3 * (5.35 * Math.Log(Concentration / 100) - 5.9) W / m2
390 = reference heat, required for a temperature of 288 K.
3 = climate feedback (water vapor and insulation from clouds)
5.9 = so that the contribution becomes 0 at 300 ppm (you reach reference heat).
The atmosphere has a mass of about 3.16 trillion tonnes at 400 ppm. So you can write:
Mass = (Concentration / 400.0) * 3.16 * 1.0E+15 / 1.0E+12
I've run the equation for several concentrations of CO2 in the atmosphere.
CO2 = 300 ppm; Heat = 390 W / m^2; Temperature = 288 K; CO2 mass (Gigatonnes) = 2370
CO2 = 600 ppm; Heat = 401 W / m^2; Temperature = 290 K; CO2 mass (Gigatonnes) = 4740
CO2 = 1200 ppm; Heat = 412 W / m^2; Temperature = 292 K; CO2 mass (Gigatonnes) = 9480
CO2 = 2400 ppm; Heat = 424 W / m^2; Temperature = 294.1 K; CO2 mass (Gigatonnes) = 18960
CO2 = 4800 ppm; Heat = 435 W / m^2; Temperature = 296 K; CO2 mass (Gigatonnes) = 37920
Mankind puts about 30/2 = 15 billion tonnes of CO2 / year into the atmosphere as of 2012. Producing 1 trillion tonnes takes about 66 years (30 = what's produced, but half goes into the ocean and the other half into the atmosphere).
It's pretty hard producing so much coal, oil and gas every year, humanity seems to be close to the maximum production rate. So in the absence of any shocking new developments that would accelerate the production of CO2 (a possible candidate for this is coal gasification), let's say that this production stays more or less constant in the future. Then we can make a timeline:
2.4 -> 4.7 trillion tonnes takes 152 years. (we are roughly at 30% of this time line)
4.7 -> 9.5 trillion tonnes takes 317 years.
9.5 -> 19 trillion tonnes takes 627 years.
19 -> 38 tillion tonnes takes 1254 years.
Although I doubt humankind can ever produce 37 trillion tonnes of CO2 (that's about 12 trillion tonnes of carbon), there are not enough recoverable reserves... unless there are new developments which gives access to more carbon.
I'll take some comfort in these numbers, that disaster is not imminent, mankind will have a long time to consider the consequences of its actions. Before climate change becomes a very big problem, other types of pollution might already have taken their toll... because the levels of CO2 production required to get a big temperature rise are mind-boggling.
One aspect of CO2 burning is the release of trace amounts of radioactivity. If we'd burn many trillions of tonnes of coal, even trace amounts become significant. (edit: although it's contained in the ashes and aren't lethal levels, so it's mostly a local storage problem).
Sulfur emissions may also become a big problem, as mankind turns to lower and lower quality of coal.
The numbers change if we consider a water vapor feedback that increases with increasing temperature. This is what happens if the water-vapor feedback would increase from a factor 2 to 3.
CO2 = 300 ppm; Heat = 390 W / m^2; Temperature = 288 K; Water vapor feedback = 2; CO2 mass (Gigatonnes) = 2370
CO2 = 600 ppm; Heat = 402 W / m^2; Temperature = 290.2 K; Water vapor feedback = 2.18; CO2 mass (Gigatonnes) = 4740
CO2 = 1200 ppm; Heat = 417 W / m^2; Temperature = 292.8 K; Water vapor feedback = 2.405; CO2 mass (Gigatonnes) = 9480
CO2 = 2400 ppm; Heat = 435 W / m^2; Temperature = 296 K; Water vapor feedback = 2.675; CO2 mass (Gigatonnes) = 18960
CO2 = 4800 ppm; Heat = 457 W / m^2; Temperature = 299.6 K; Water vapor feedback = 3.005; CO2 mass (Gigatonnes) = 37920
This may seem exaggerrated, but water vapor pressure more than doubles when temperatures rises 10 degrees.
Of course this asummes that albedo (from clouds) remains constant. It's not know whether there will be more or fewer clouds if temperatures increase.
I wonder about changes of the upper boundary of the atmosphere. The height of the troposphere (where upper clouds form) ranges from about 7 km (during winter at the poles) to about 20 km (in the tropics). How does such a change in the troposphere affect temperatures?