The relationship between temperature and the mechanical properties of an end cross-linked equal molar random copolyether elastomer of 3,3-bis(azidomethyl)oxetane and tetrahydrofuran (P(BAMO-r-THF)) was investigated. During this investigation, the performances of two P(BAMO-r-THF) elastomers with different thermal histories were compared at different temperatures. The elastomer as prepared at 20 °C (denoted as S0) exhibited semi-crystallization morphology. Wide angle X-ray diffraction analysis indicated that the crystal grains within elastomer S0 result from the crystallization of BAMO micro-blocks embedded in P(BAMO-r-THF) polymeric chains, and the crystallinity is temperature irreversible under static conditions. After undergoing a heating-cooling cycle, this elastomer became an amorphous elastomer (denoted as S1). Regarding mechanical properties, at 20 °C, break strains and stresses of 315 ± 22% and 0.46 ± 0.01 MPa were obtained for elastomer S0; corresponding values of 294 ± 6% and 0.32 ± 0.02 MPa were obtained for elastomer S1. At −40 °C, these strains and stresses simultaneously increased to 1085 ± 21% and 8.90 ± 0.72 MPa (S0) and 1181 ± 25% and 10.23 ± 0.44 MPa (S1), respectively, owing to the strain-induced crystallization of BAMO micro-blocks within the P(BAMO-r-THF) polymeric chains.