A fundamental prediction of inflation is a nearly scale-invariant spectrum of gravitational wave. The features of such a signal provide extremely important information about the physics of the early universe. In this paper, we focus on several topics about warm inflation. First, we discuss the stability property about warm inflation based on nonequilibrium statistical mechanics, which gives more fundamental physical illustrations to thermal property of such model. Then, we calculate the power spectrum of gravitational waves generated during warm inflation, in which there are three components contributing to such spectrum: thermal term, quantum term and cross term combining the both. We also discuss some interesting properties about these terms and illustrate them in different panels. As a model different from cold inflation, warm inflation model has its individual properties in observational practice, so we finally give a discussion about the observational effect to distinguish it from cold inflation.