A catheter comprises a heater control supplying power, a handle, a base catheter with lumen and comprising a proximal section and a distal segment, and a variable stiffness element. The element comprises a heater connected to the heater control, coiled at least at the distal segment, and comprising a shaft portion of a first metallic conductive material and a heater portion of a second metallic conductive material. A jacket is disposed about the heater portion. A variable flex sub-assembly between the catheter and jacket comprises a non-conducting braid and a binding material. Without power, the binding material is stiffened. Responsive to heating of the binding material, the binding material softens to increase flexibility of the variable flex sub-assembly at least at the distal segment. Responsive to removing power, the binding material cools and stiffens to decrease flexibility of the variable flex sub-assembly at least at the distal segment.