Modelling dynamic heterogeneity in amorphous shape memory polymers (SMPs) is a huge challenge due to the complex statistics of strain energy distributions during their thermodynamic relaxations. In this study, based on the dynamic heterogeneity of strain energy distribution, we have considered, for the first time, the influences of different temperature rates and strain rates on strain energy evolution as a dynamic equilibria, rather than a quasi-static problem. We propose a phase transition model incorporated with Gaussian distribution statistics to investigate the dynamic equilibria with glass transition heterogeneity and tailorable mechanics for the amorphous SMPs. The Gaussian distribution statistics is firstly applied to characterize the heterogeneity of strain energy distributions in the amorphous polymers. Phase transition theory is then developed to describe working principles of strain energy evolution, glass transition heterogeneity, thermodynamic relaxation and tailorable mechanics. Finally, the dynamic equilibria of heterogeneity about the statistics of strain energy distribution are formulated based on the one dimensional Maxwell multi-branch model. The analytical results are compared with the experimental data of epoxy, polyamide and vinylester SMPs reported in literature, and good agreements between them are demonstrated. This study provides a new insight into the dynamic heterogeneity in the mechanics of amorphous SMPs.