Curcumin (Cur) is a beneficial ingredient with numerous bioactivities. However, due to its low solubility and poor bioavailability, its therapeutic application is limited. In this work, we prepared poly-N-isopropylacrylamide p(NIPAm) and polyallylamine p(Am)-based nanogel (p(NIPAm-co-Am)) NG for a dual pH- and temperature-sensitive copolymer system for drug delivery application. In this copolymer system, the p(NIPAm) segment was incorporated to introduce thermoresponsive behavior and the p(Am) segment was incorporated to introduce drug binding sites (amine groups) in the resulting (p(NIPAm-co-Am)) NG system. Various instrumental characterizations including 1H nuclear magnetic resonance (1H NMR) spectroscopy, Fourier transform infrared (FT-IR) analysis, scanning electron microscopy (SEM), zeta potential, and particle size analysis were performed to confirm the copolymer synthesis. Curcumin (Cur), an anticancer bioactive substance, was employed to assess the in vitro drug loading and release performance of the resulting copolymer nanogels system at varied pH levels (pH 7.2, 6.5, and 4.0) and temperatures (25 °C, 37 °C, and 42 °C). The cytocompatibility of the p(NIPAm-co-Am) NG sample was also tested on MDA-MB-231 cells at various sample concentrations. All the study results indicate that the p(NIPAm-co-Am) NG produced might be effective for drug loading and release under pH and temperature dual-stimuli conditions. As a result, the p(NIPAm-co-Am) NG system has the potential to be beneficial in the use of drug delivery applications in cancer therapy.