Kiwistonewall,
Certainly Mars has more CO2 than earth, and the effect of this CO2 does not seem to be the same as on Earth which is not surprising given the different drivers of the two atmospheres.
But your analysis does have a number of flaws including ignoring the logarithmic effect of CO2 that sceptics keep reminding me of!
1) First you need to calculate the effective temperature that Earth and Mars need to be to radiate away the solar energy it absorbs. The results for Earth and Mars are:
Earth's temperature is 253 Kelvin
Mars' temperature is 211 Kelvin
2) Then calculate the effect of the greenhouse gases. On earth, the effect of 280ppm was to raise temperatures about 33C. About 20-30% of this is due to CO2 - so about 7-10C. The models then predict a further 1C rise (before feedbacks) for each doubling from 280ppm.
There is about 24 times 280ppm of CO2 per column of atmosphere which is about 4.5 doublings. So we'd expect temps of about 4.5C plus the original 7-10C = 11-15C more than Mars' predicted temperature of 211 - so 220-225 Kelvin for the surface of Mars.
Details below:
TSI is 1365W/m^2 at Earth's orbit. You need to divide by 4 to average over the whole earth's surface, which gives 341:
1365 * (area of earth's disk exposed to the sun = pi * radius squared) divided by area of earth = 4*pi*radius squared) = 1364/4 = 341W/m^2
Earth albedo is about 0.31 so it reflects 31% of the radiation and absorbs on average 69% which is 235 W/m^2.
If we take your figure of 39% TSI at Mars' orbit, and include Mars' lower albedo (15%) such that it absorbs 85% of the radiation it receives, then Mars absorbs 235 * 0.39 * (0.85/0.69) = 113W/m^2.
To keep to a stable temperature, Earth and Mars must emit about the same amount of energy as they absorb. You can calculate the approximate temperature they need to be to radiate the balancing energy.
Based on Stephan-Boltzman, the effective temperature of the object is approx given by the formula
Energy = sigma * T^4
Where sigma is 5.67e-8 W/m^2/K^4. So effective temperature:
Te = fourth root of (energy/5.67e-8)
From the above calculation:
Earth's temperature is 253 Kelvin
Mars' temperature is 211 Kelvin
As we know the surface temperature of the earth is about 285 Kelvin on average this leads to the given "greenhouse" warming of just over 30 degrees. This is an empirical result though which comes about due to the particular structure of the earth's atmosphere.
2) Then you need to calculate the effect of the greenhouse warming.
If the earth is, say 33C warmer due to the whole greenhouse effect, and 20% of this is due to CO2, then the effect of the CO2 is about 7C of this.
Based on empirical evidence and radiation calculations, a doubling from 280ppm to 560ppm of CO2 is expected to cause a temperature rise of 1C before feedbacks.
From Kiwistonewall's figures Mars has about 24 times the 280ppm we "started" with 250 years ago. This equates to about 4.5 doublings of CO2 relative to earth.
So Mars temperature should be an extra 4.5C warming on top of the 7C, which is 11.5C.
So we might expect Mars to have an "average" temperature in the region of 222 Kelvin.