During the conclave itself, there is likely not much conversation going on since it is mainly for prayer and election. The official prayers are said in Latin, as are all of the statements and questions prescribed in the rules governing the conclave, including the oath that the cardinals swear at the beginning of the conclave, and the declaration each cardinal makes when casting his vote.
The cardinals may talk among themselves in their native languages back at the residence. Because Latin is the universal language of the Church, it is not beyond the realm of possibility that they could talk among themselves using Latin. Additionally, many of the cardinals know Italian, since it is the language of the Curia.
In their General Congregation meetings before the conclave, the cardinals had at their disposal simultaneous translation in five languages: Italian, English, Spanish, French and German, so it seems that each cardinal spoke in a language most comfortable to him.