For those who love equations:
An equation for estimating the mean temperature on the surface of Mars as a function of the CO2 atmospheric pressure and the solar constant is given by McKay and Davis [1] as:

Tmean = S^0.25xTBB + 20(1+S)P^0.5 (Eq.1)

where Tmean is the mean planetary temperature in kelvins, S is the solar constant where the present day Sun=1, TBB, the black body temperature of Mars at present = 213.5 K, and P is given in bar.

Since the atmosphere is an effective means of heat transport from the equator to the pole,we propose (as an improvement over equation (1) in reference [2]:

Tpole = Tmean - DT/(1 + 5P) (Eq. 2)

where DT is what the temperature difference between the mean value and the pole would be in the absence of an atmosphere (about 75 K for S=1).

For purposes of this analysis it is further assumed based upon a rough approximation to observed data that :

Tmax = Tequator = 1.1Tmean (Eq. 3)

and that the global temperature distribution is given by:

T(q) = Tmax - (Tmax-Tpole)sin^1.5q (Eq.4)

where q is the latitude (north or south).

Equations (1) through (4) given the temperature on Mars as a function of CO2 pressure. However, as mentioned above, the CO2 pressure on Mars is itself a function of the temperature. There are three reservoirs of CO2 on Mars, the atmosphere, the dry ice in the polar caps, and gas adsorbed in the soil. the interaction of the polar cap reservoirs with the atmosphere is well understood and is given simply by the relationship between the vapor pressure of CO2 and the temperature at the poles. This is given by the vapor pressure curve for CO2, which is approximated by:

P = 1.23 x 10^7{exp(-3168/Tpole)} (Eq. 5)

So long as there is CO2 in both the atmosphere and the cap, equation (5) gives an exact answer to what the CO2 atmospheric pressure will be as a function of polar temperature. However if the polar temperature should rise to a point where the vapor pressure is much greater than that which can be produced by the mass in the cap reservoir (between 50 and 150 mb) then the cap will disappear and the atmosphere will be regulated by the soil reservoir.

The relationship between the soil reservoir, the atmosphere and the temperature is not known with precision. an educated guess is given in parametric form in reference 1 as:

P = {CMaexp(T/Td)}1/g (6)

where Ma is the amount of gas adsorbed in bar, g=0.275, C is a normalization constant set so that with chosen values of the other variables equation (6) will reflect known Martian conditions, and Td is the characteristic energy required for release of gas from the soil. Equation (6) is essentially a variation on Van Hofft's law for the change in chemical equilibrium with temperature, and so there is fair confidence that its general form is correct. However the value of Td is unknown and probably will remain so until after human exploration of Mars. In reference [2] McKay et al varied parametrically Td from 10 to 60 K and produced curves using equation (6) with T set equal to either Tpole or Tmean. In this paper we choose Td=15 to 40 K (a reasonable subset of the spectrum slightly on the optimistic side; the lower the value of Td the easier things are for prospective terraformers.) Because equation (6) is so strongly temperature dependent, however, we do not simply set T to the extreme values of Tmean or Tpole and solve equation (6) to get a global "soil pressure" however, as was done in reference [2]. Rather we use the global temperature distribution given by equation (4) to integrate equation (6) over the surface of the planet. This gives a more accurate quasi 2-Dimensional view of the atmosphere/regolith equilibrium problem in which most of the adsorbed CO2 is distributed to the planet's colder regions. In this model, regional (in the sense of latitude) temperature changes, especially in the near-polar regions, can have as important a bearing on the atmosphere/regolith interaction as changes in the planet's mean temperature.