Shape‐memory polymers (SMPs) that respond near body temperature are attracting broad interest, especially in the biomedical fields. In this study, the triggering temperature of poly(caprolactone) SMP networks is precisely adjusted by inclusion of non‐crystallizable molecular linkers and by variation of prepolymer molecular weight. Longer, non‐crystalline linkers and lower molecular weight prepolymers interfere with crystallization, lowering the transition temperature. Networks are prepared with crystallization temperatures that are beneath the human body temperature and yet are above room temperature. Upon cooling such amorphous networks to room temperature, crystallization is sluggish. There, elastomers can be easily strained by several hundred‐percent to induce crystallization, thereby fixing strained states. If subsequently heated, programmed SMPs can release significant amounts of stored strain energy (∼3 MJ/m3). SMPs that combine elastic energy storage and exhibit triggering temperatures near the human body temperature could benefit emerging applications in the biomedical space. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 1397–1404