This paper deals with the automatic analysis of conversations between a customer and an agent in a call centre of a customer care service. The purpose of the analysis is to hypothesize themes about problems and complaints discussed in the conversation. Themes are defined by the application documentation topics. A conversation may contain mentions that are irrelevant for the application purpose and multiple themes whose mentions may be interleaved portions of a conversation that cannot be well defined. Two methods are proposed for multiple theme hypothesization. One of them is based on a cosine similarity measure using a bag of features extracted from the entire conversation. The other method introduces the concept of thematic density distributed around specific word positions in a conversation. In addition to automatically selected words, word bigrams with possible gaps between successive words are also considered and selected. Experimental results show that the results obtained with the proposed methods outperform the results obtained with support vector machines on the same data. Furthermore, using the theme skeleton of a conversation from which thematic densities are derived, it will be possible to extract components of an automatic conversation report to be used for improving the service performance.