Additively manufactured (3D-printed) elastomers have increasing applications in impact resistance devices such as helmets, shoe soles, and shock absorbing architectured metamaterials. These rapidly expanding areas require a proper understanding of the thermo-mechanical behaviours of soft polymers. In this contribution, thermal–mechanical properties of 3D-printed elastomeric polyurethane (EPU) are extensively characterised under low to high strain rates which are missing in the literature. The EPU under investigation is digitally manufactured using a Digital Light Synthesis (DLS) technology and is characterised by tensile experiments with a wide range of strain rates spanning from 0.001/s to 500/s and temperature variations of -20 °C to 60 °C. The experimental results reveal deformation nonlinearity, thermal-sensitivity, and strain rate-sensitivity in the elastomer. Moreover, the study reveals the occurrence of the glass transition phenomenon, which is commonly observed in soft materials under low-temperature and high strain-rate conditions. Various graphical illustrations are presented to depict the effects of temperature and strain rate on the stress response. It is observed that as temperature decreases or strain rate increases, the stress amplifies and becomes more sensitive to variations in temperature or strain rate. Additionally, higher strain levels further enhance the stress sensitivity to these variations. The microscopic mechanisms behind the thermal and strain rate sensitivities are discussed, taking into account the influence of the strain level. Overall, this study contributes to a proper understanding of the thermo-mechanical behaviours of digitally-printed soft polymers, particularly in dynamic scenarios.