<p>Laminate plates are frequently used structural elements in many branches of engineering. The understanding of their dynamic behaviour under various service conditions is of great importance. This paper is devoted to the free vibration analysis of such plates containing orthotropic elastic faces and viscoelastic layers, which are useful in reducing excessive vibrations. One of key problems in this aspect is the influence of varying ambient temperature on the properties of available viscoelastic materials. In the proposed analyses the notorious time–temperature superposition and four different methods of thermal shift computation are considered. The plate kinematics is described with the refined zig-zag theory. The Zener fractional physical law with the split of volumetric and deviatoric parts of deformation for viscoelastic layers is used with the elastic model retrieved as a special case, where the orthotropy of the material can be introduced. The free vibration problem of layered plates is formulated using the principle of virtual work and the finite element discretisation. The paper presents the results and discussion of several numerical examples solved using the proposed approach. They include: verification of the static and dynamic solutions by comparison with available literature results, comparisons of various methods of temperature effect inclusion, verification of the orthotropy level influence and checking the behaviour of various VE materials used as a core layer in laminates with orthotropic faces.</p>