Polymers are nowadays often used in the process of manufacturing of numerous products and components. The knowledge of material parameters is essential for proper sizing of products. This is especially the case with regards to modulus of elasticity. In the case of polymers, the latter is well known to vary with temperature. The standard approach, which is based on clamping test samples, appears to cause creep-related issues at elevated temperatures. The paper presents a non-contact method, which is not sensitive to creep and enables the identification of the elasticity modulus based on experimentally obtained natural frequencies. This is done by utilizing an alternative clamping method of the test sample which imposes free boundary conditions. The natural frequencies were identified in the temperature range from 30 °C to 120 °C, which are used for calculating the modulus of elasticity at these temperatures. Viscous damping ratio was also identified in the same temperature range.