We construct a simple model for the emission-line profiles of CO from the circumstellar envelope (CSE) of the carbon-rich star IRC +10216. Using the Sobolev approximation, and a given gas temperature distribution (gTD) we construct simulated observations of this source. We find that the 'canonical' gTD [T(r)proportional to r(-0.7)] cannot reproduce the observations. Guided by a strong correlation between telescope beamsize and peak intensity, we vary the gTD to fit the observations, and find that the data are best reproduced by T(r) proportional to r(-1). This power law is consistent with CO line radiation being the dominant coolant in the CSE. Differences between this and other results may be the result of a previous lack of high-resolution observations, the use of older CO collisional rates, or reduced mass-loss rate. Although an assumed source distance of 150 pc gives the best fit to the data, we cannot rule out the possibility of a larger source distance (e.g. 300 pc).