The success of stretchable electronics based on conjugated polymers relies on having a thorough understanding of the polymer's mechanical behavior over conditions likely encountered during operation. To meet this need, a novel approach to capture the stress-strain response of thin conjugated polymer films is introduced. This is achieved by laminating the polymer film of interest on a thin elastomer substrate and testing the composite specimen in a dynamic mechanical analyzer in a tensile test configuration. We term this approach as film laminated on thin elastomer (FLOTE) method. The benefits of this method include the ability to (1) determine the viscoelastic behavior of the conjugated polymer by testing over a broad range of temperatures and strain rates, (2) measure the film behavior over large cyclic strains, including under in-plane compression, and (3) capture the impact of the neighboring elastomer on the behavior of the polymer film. The focus is on the widely studied poly(3-hexylthiophene) (P3HT) as a model system. We find that the viscoelastic characteristics of P3HT, varied by changing the specimen temperature, significantly impact film stability under cyclic strain. This includes showing that the hysteresis behavior of the films under cyclic strain changes significantly with sample temperature. In addition, it is found that, under cyclic loading, the composite has features consistent with Mullins' effect. Based on these results, insights into polymer viscoelastic characteristics necessary to achieve high-performance stretchable electronics are gained.