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The paper is devoted to the analysis of the influence of ambient temperature on the linear free and non-linear harmonic vibrations of laminate plates with viscoelastic layers. The Zener fractional material model is adopted. The plate kinematics is described using the refined zig-zag theory. The formulation of vibrations of the plate is based on the physical law with the separation of deviatoric and volumetric deformation. The temperature influence is included using the frequency-temperature superposition principle. The shift factor applied to modify the damping properties of the viscoelastic material is computed using the Willams-Landel-Ferry formula. The paper contains the results of several analyses of laminate plates with various viscoelastic materials for which the material data were available in the literature. In particular, the analyses focus on determination of the properties characteristic for the plates with Zener fractional model under the influence of the ambient temperature. • Frequency-temperature superposition for temperature influence on plates vibrations • Refined zig-zag theory applied to define the plate kinematics • Fractional Zener material with separated volumetric and deviatoric deformation • Numerous analyses of various viscoelastic materials • Explanation of non-monotonous character of temperature effects on damping [ABSTRACT FROM AUTHOR]