Understanding the effect of cold storage on arterial tissues is essential in various clinical and experimental practices. Cold storage techniques could significantly affect the post-cryosurgical or post-cryopreservation mechanical behavior of arteries. Previously, arteries were considered homogenous and elastic and the changes in material properties due to cold storage were inconclusive. In this study, using a custom-made nanoindentation device, changes to the local viscoelastic properties of porcine thoracic aorta wall due to three common storage temperatures (+4, -20, and -80 °C) within 24 h, 48 h, 1 week, and 3 weeks were characterized. The changes to both elastic and relaxation behaviors were investigated considering the multilayer, heterogeneous nature of the aortic wall. The results showed that the average instantaneous Young's modulus (E) of +4 °C storage samples decreased while their permanent average relaxation amplitude (G (∞)) increased and after 48 h these changes became significant (10 and 13% for E and G (∞), respectively). Generally, in freezer storage, E increased and G (∞) showed no significant change. In prolonged preservation (>1 week), the results of -20 °C showed significant increase in E (20% after 3 weeks) while this increase for -80 °C was not significant, making it a better choice for tissue cold storage applications.