A shape memory polymer traditionally refers to a polymer that can memorize one temporary shape and recover to its permanent shape upon exposure to an external stimulus. Although this basic concept has been known for at least half a century, recent advances have led to the discoveriy of previously uncovered memory properties that challenge the traditional concept of shape memory polymers. In particular, a temperature memory effect refers to the capability of a polymer to memorize temperatures instead of shapes. Thus far, the reported temperature memory effect has been established under iso-strain stress recovery conditions, in which the maximum recovery stress appears at a temperature roughly identical to the deformation temperature. This effect can be called recovery stress based temperature memory effect. In this work, experiments were designed in an attempt to establish a temperature memory effect based on the stress free strain recovery behaviors of Nafi on. The results show that, under carefully selected conditions, the temperature at which a maximum strain recovery rate is observed can indeed be quantitatively related to the deformation temperature. In addition, indications that the polymer is capable of memorizing more than one deformation temperature (i.e., multi-temperature memory effect) are shown. The molecular origin of Nafi on's temperature memory effect is elucidated through small angle neutron scattering study.