The incorporation of unnatural amino acids (uAAs) into protein‐based polymers has emerged as a powerful methodology to expand their chemical repertoire. Recently, we demonstrated that incorporating uAAs into two temperature‐responsive protein‐based polymers—namely resilin‐ and elastin‐like polypeptides (RLPs and ELPs, respectively)—can alter their properties. In this study, we incorporated aromatic uAAs into the protein sequence of RLP–ELP diblocks to yield new and diverse assemblies from a single DNA template. Specifically, we show that incorporating aromatic uAAs can modulate the phase‐transition behaviors and self‐assembly of the diblocks into various morphologies, including spherical and cylindrical micelles and single‐ and double‐layered vesicles, with some constructs also demonstrating a temperature‐responsive shape‐shifting behavior. Next, we evaluated the ability of the RLP–ELP assemblies to encapsulate a chemotherapeutic drug, doxorubicin, and show how the identity of the incorporated uAAs and the morphology of the nanostructure affect the encapsulation efficiency. Taken together, our findings demonstrate that the multi‐site incorporation of uAAs into temperature‐responsive, amphiphilic protein‐based diblock copolymers is a promising approach for the functionalization and tuning of self‐assembled nanostructures.