Remote magnetic navigation of catheters is a technique used to perform radiofrequency ablation of heart tissue in order to treat cardiac arrhythmias. The flexible magnetic catheters used in this context are in some cases not sufficiently dexterous to navigate the complex and patient- specific anatomy of the heart. To overcome such limitations, this paper proposes a new approach that relies on the integration of variable stiffness segments into a magnetic catheter. The magnetic variable stiffness (VS) catheter presented here is based on silicone and a low melting point alloy (LMPA) that transforms from a solid to liquid phase upon joule heating. This dramatically changes the bending stiffness of the segment in which it is integrated, improving dexterity. Compared to standard catheters, a VS catheter can partially (just one segment) or completely lock its shape (shape fixity) in order to explore a larger 3D volume inside a magnetic navigation system, thus extending regions of the heart that can be reached for performing ablation procedures.