Innate and adaptive immune responses lead to wound healing by regulating a complex series of events promoting cellular cross-talk. An inflammatory response is presented with its characteristic clinical symptoms: heat, pain, redness, and swelling. Some smart thermo-responsive polymers like chitosan, polyvinylpyrrolidone, alginate, and poly(ε-caprolactone) can be used to create biocompatible and biodegradable scaffolds. These processed thermo-responsive biomaterials possess 3D architectures similar to human structures, providing physical support for cell growth and tissue regeneration. Furthermore, these structures are used as novel drug delivery systems. Locally heated tumors above the polymer lower the critical solution temperature and can induce its conversion into a hydrophobic form by an entropy-driven process, enhancing drug release. When the thermal stimulus is gone, drug release is reduced due to the swelling of the material. As a result, these systems can contribute to the wound healing process in accelerating tissue healing, avoiding large scar tissue, regulating the inflammatory response, and protecting from bacterial infections. This paper integrates the relevant reported contributions of bioengineered scaffolds composed of smart thermo-responsive polymers for drug delivery applications in wound healing. Therefore, we present a comprehensive review that aims to demonstrate these systems’ capacity to provide spatially and temporally controlled release strategies for one or more drugs used in wound healing. In this sense, the novel manufacturing techniques of 3D printing and electrospinning are explored for the tuning of their physicochemical properties to adjust therapies according to patient convenience and reduce drug toxicity and side effects.