Synthetic cell models help us understand living cells and the origin of life. Key aspects of living cells are crowded interiors where secondary structures, such as the cytoskeleton and membraneless organelles/condensates, can form. These can form dynamically and serve structural or functional purposes, such as protection from heat shock or as crucibles for various biochemical reactions. Inspired by these phenomena, we introduce a crowded all-DNA protocell and encapsulate a temperature-switchable DNA-b-polymer block copolymer, in which the synthetic polymer phase-segregates at elevated temperatures. We find that thermoreversible phase segregation of the synthetic polymer occurs via bicontinuous phase separation, resulting in artificial organelle structures that can reorient into larger domains depending on the viscoelastic properties of the protocell interior. Fluorescent sensors confirm the formation of hydrophobic compartments, which enhance the reactivity of bimolecular reactions. This study leverages the strengths of biological and synthetic polymers to construct advanced biohybrid artificial cells that provide insights into phase segregation under crowded conditions and the formation of organelles and microreactors in response to environmental stress.