Model Order Reduction (MOR) methods such as Component Mode Synthesis (CMS) have been used in order to simulate large linear dynamic systems for many years and have reached a considerable level of saturation. These reduction methods have many advantages such as minimizing the computational costs but also have restrictions. One of their disadvantages is that material damping characteristics can only be defined in form of Rayleigh damping. Another disadvantage is that the reduced model can only represent one state of the structure determined in the generation process of the reduced matrices. In this paper we present a way to consider material damping in reduced matrices that contain one or more materials having different damping characteristics without the disadvantages of using Rayleigh damping. Further using the matrices of the reduced structure in the initial state and the change of the content of the matrices with respect to the change of material properties due to viscoelasticity we successfully model the frequency and temperature dependent behavior of structures containing one viscoelastic material such as rubber and possibly other linear elastic materials. Numerical experiments are carried out in order to investigate the accuracy and efficiency of the developed algorithms by comparing the harmonic response of full viscoelastic finite element models with reduced models using CMS. This improved functionality will offer an efficient and more accurate numerical description of the NVH behavior of complex structures such as electrical motors.