Polymeric micelles and especially those based on natural diblocks are of particular interest due to their advantageous properties in terms of molecular recognition, biocompatibility, and biodegradability. We herein report a facile and straightforward synthesis of thermoresponsive elastin-like polypeptide (ELP) and oligonucleotide (ON) diblock bioconjugates, ON-b-ELP, through copper-catalyzed azide-alkyne cycloaddition. The resulting thermosensitive diblock copolymer self-assembles above its critical micelle temperature (CMT ∼30 °C) to form colloidally stable micelles of ∼50 nm diameter. The ON-b-ELP micelles hybridize with an ON complementary strand and maintain their size and stability. Next, we describe the capacity of these micelles to bind proteins, creating more complex structures using the classic biotin-streptavidin pairing and the specific recognition between a transcription factor protein and the ON strand. In both instances, the micelles are intact, form larger structures, and retain their sensitivity to temperature.