New observations of the CO J = 3-2 emission in the circumstellar envelope of IRC +10216 are presented. Strips maps of this source have been obtained at 0.5 arcmin spacing with an optical telescope, which allows the beam pattern to be determined very accurately. The observations are compared with the predictions of the standard thermal model of Kwan and Linke (1982), and the model and the observations are found to agree very well. However, the model predicts that the effective J = 3-2 source is much smaller than the beam size. It is concluded that the observations cannot further constrain the input parameters of the Kwan and Linke model.