Due to its sensitivity to temperature and the significant influence on vibration isolation performance, it is crucial to investigate the dissipation characteristic and parameter identification of metal rubber vibration isolation structure in thermal environments. In this study, a dual-layer metal rubber vibration isolation structure is designed. The influence of environmental temperature on the dissipation characteristic of the isolation structure is investigated. A nonlinear constitutive model for the dual-layer metal rubber isolation structure is established. At first, a series of dissipation characteristic tests are conducted on the isolation structure at different temperatures. Dissipation characteristic curves of the isolation structure under various operating conditions are obtained. The dissipation coefficient, dissipated energy, and maximum deformation potential energy are calculated. The effects of temperature, amplitude, and frequency on the dissipation characteristic of the dual-layer metal rubber isolation structure are analyzed. Then, the parameters of the isolation structure are identified using nonlinear least squares method. A nonlinear functional constitutive model for the metal rubber isolation structure is established. It can accurately predict the dissipation characteristic curves of the isolation structure under different operating conditions.