Two new thermoresponsive self-healing polyurethanes (1DA1T and 1.5DA1T) based on the Diels-Alder (DA) reaction between furan and maleimide moieties are developed that use the shape-memory effect to bring crack faces into intimate contact such that healing can take place. Unlike other self-healing polymers, these polymers do not require external forces to close cracks but rather they use the shape-memory effect to autonomously close the crack. Both polyurethanes have a stable polymer structure and comparable mechanical properties to commercial epoxies. A differential scanning calorimeter is employed to check the glass transition temperature of the polymers as well as the DA and retro-DA (rDA) reaction temperatures. These DA and rDA reactions are confirmed with variable-temperature proton nuclear magnetic resonance. Healing efficiency is calculated using a measurement of the failure load from compact tension testing. The results show that the shape-memory effect can replace external forces to close two crack surfaces and the DA reaction can be repeatedly employed to heal the cracks.