This exploratory case study aimed to investigate patterns in student reasoning in statistical mechanics, in order to identify difficulties and develop ideas for future research. Upper-division undergraduate students, taking a course in statistical mechanics, were interviewed in groups. Here we present observed patterns of student reasoning about a simple, discrete system in contact with a heat bath. Our findings reveal problematic student intuitions of the high temperature limit. Several students were, however, able to transfer knowledge from a similar problem involving spin to improve their reasoning.