Thermoresponsive polymers exhibiting lower critical solution temperatures (LCSTs) in aqueous solution have garnered considerable attention for the development of smart materials. Herein, we report the synthesis and properties of pH-tunable thermoresponsive poly(ethylene oxide) (PEO)-based functional polymers bearing pendant amine groups with varying cloud points. Well-defined poly(ethylene oxide-co-allyl glycidyl ether) (P(EO-co-AGE)) copolymers were prepared via controlled anionic ring-opening copolymerization of ethylene oxide (EO) with 10 mol % of a functional allyl glycidyl ether (AGE) comonomer. Facile, modular thiol–ene click chemistry was then employed to introduce a library of different aminothiols as side chains to the initial P(EO-co-AGE) copolymer. Depending on the nature of the pendant amine groups (primary amine, dimethylamine, and diethylamine) and the hydrophobicity of the side chains (ethyl, propyl, and hexyl), the cloud points could be tuned from 44–100 °C under different pH conditions. This is the first systematic investigation into the effect of PEO copolymer side chains on cloud point, which opens up the opportunity to make new thermoresponsive polymers for a variety of smart material applications.