Variable stiffness (VS) is an important feature that significantly enhances the dexterity of magnetic catheters used in minimally invasive surgeries. Existing magnetic catheters with VS consist of sensors, heaters, and tubular structures filled with low melting point alloys, which have a large stiffness change ratio but are toxic to humans. In this paper, a VS magnetic catheter is described for minimally invasive surgery; the catheter is based on a novel variable stiffness thread (VST), which is made of a conductive shape memory polymer (CSMP). The CSMP is nontoxic and simultaneously serves as a heater, a temperature sensor, and a VS substrate. The VST is made through a new scalable fabrication process, which consists of a dipping technique that enables the fabrication of threads with the desired electrical resistance and thickness (with a step size of 70 µm). Selective bending of a multisegmented VST catheter with a diameter of 2.0 mm under an external magnetic field of 20 mT is demonstrated. Compared to existing proof-of-concept VS catheters for cardiac ablation, each integrated VST segment has the lowest wall thickness of 0.75 mm and an outer diameter of 2.0 mm. The segment bends up to 51° and exhibits a stiffness change factor of 21.