Content analysis of mass media publications has become a major scientific method used to analyze public discourse on climate change. We propose a computer-assisted content analysis method to extract prevalent themes and analyze discourse changes over an extended period in an objective and quantifiable manner. The method includes the following: (1) sample selection; (2) preparation of the text segments for computer processing; (3) identifying themes in the texts using exploratory factor analysis; (4) combining identified themes into higher order themes using confirmatory factor analysis; (5) using factor scores to interpret themes obtained from public discourse; and (6) tracking the main themes of public discourse through time. We apply the proposed methodology to the analysis of the articles published in the New York Times on climate change during the period from 1995 to 2010. We found a gradual decline in the volume of material within the "Science" topic and an expansion of themes classified under the "Politics" topic.