Polymers exhibit complex mechanical behavior. Rubber or similar materials are known to display both viscoelasticity and nonlinear elasticity. However, quasi-static mechanical tests alone are insufficient for capturing the viscous component of their response. While Dynamic Mechanical Analysis (DMA) provides valuable insights, it is inadequate to characterize the material's behavior under large deformations fully. A hybrid approach combining a quasi-static tensile test with modulation is proposed to address these limitations. During these tests, deformation fields obtained via Digital Image Correlation (DIC) can be complemented by infrared thermography. The experimental setup is based on a modified DY22 universal testing machine. Tests were performed on a rubber band designed for sports applications. The mechanical results, including the load-elongation relationship and field measurements, reveal distinct differences between the quasi-static and modulated components. These differences are particularly evident in the evolution of the elastic modulus and Poisson's ratio as a function of elongation. The measurements provide detailed insights into the material's mechanical response at each loading stage. The results demonstrate that integrating modulated testing techniques with thermomechanical analysis allows for a more comprehensive characterization of materials for engineering applications.