This paper introduces a real-time path optimization and control strategy for shape memory alloy (SMA) actuated cardiac ablation catheters, potentially enabling the creation of more precise lesions with reduced procedure times and improved patient outcomes. Catheter tip locations and orientations are optimized using parallel genetic algorithms to produce continuous ablation paths with near normal tissue contact through physician-specified points. A nonlinear multivariable control strategy is presented to compensate for SMA hysteresis, bandwidth limitations, and coupling between system inputs. Simulated and experimental results demonstrate efficient generation of ablation paths and optimal reference trajectories. Closed-loop control of the SMA-actuated catheter along optimized ablation paths is validated experimentally.