The aim of this study was to develop an innovative, dual-stimuli-responsive smart hydrogel local drug delivery system (LDDS), potentially useful as an injectable simultaneous chemotherapy and magnetic hyperthermia (MHT) antitumor treatment device. The hydrogels were based on a biocompatible and biodegradable poly(ε-caprolactone-co-rac-lactide)-b-poly(ethylene glycol)-b-poly(ε-caprolactone-co-rac-lactide) (PCLA-PEG-PCLA, PCLA) triblock copolymer, synthesized via ring-opening polymerization (ROP) in the presence of a zirconium(IV) acetylacetonate (Zr(acac)4) catalyst. The PCLA copolymers were successfully synthesized and characterized using NMR and GPC techniques. Furthermore, the gel-forming and rheological properties of the resulting hydrogels were thoroughly investigated, and the optimal synthesis conditions were determined. The coprecipitation method was applied to create magnetic iron oxide nanoparticles (MIONs) with a low diameter and a narrow size distribution. The magnetic properties of the MIONs were close to superparamagnetic upon TEM, DLS, and VSM analysis. The particle suspension placed in an alternating magnetic field (AMF) of the appropriate parameters showed a rapid increase in temperature to the values desired for hyperthermia. The MIONs/hydrogel matrices were evaluated for paclitaxel (PTX) release in vitro. The release was prolonged and well controlled, displaying close to zero-order kinetics; the drug release mechanism was found to be anomalous. Furthermore, it was found that the simulated hyperthermia conditions had no effect on the release kinetics. As a result, the synthesized smart hydrogels were discovered to be a promising antitumor LDDS, allowing simultaneous chemotherapy and hyperthermia treatment.