Analogy is an important innovative thought. Utilizing educational value of analogy thought, and strengthening students' analogy thought training are helpful to the cultivation of innovative talents. In this paper, viscoelastic mechanics and generalized heat conduction are used to show design case of analogy thought teaching used in continuum mechanics. Firstly, based on elastic unit and viscous unit of mechanics, the series-parallel method is used to derive the viscoelastic Maxwell model and Kelvin-Voigt model. Secondly, the generalized heat transfer Cattaneo-Vernotte model and Green-Naghdi model are given, and the origin of the concept of thermal displacement in Green-Naghdi model is introduced. Subsequently, "elastic" and "viscous" units of thermal science are introduced by analogy, series-parallel method is applied to realize the reconstruction of Cattaneo-Vernotte model and Green-Naghdi model, and the analogy relationship between viscoelastic mechanics and generalized heat conduction is clarified. Finally, the differences between fundamental equations of thermal science and mechanics are analyzed, and it is pointed out that attention to the differences between research objects is the important approach of creative analogical thinking.