Robotic surgery is being used widely due to its various benefits that includes reduced patient trauma and increased dexterity and ergonomics for the operating surgeon. Making the whole or part of the surgical procedure autonomous increases patient safety and will enable the robotic surgery platform to be used in telesurgery. In this work, an Electrosurgery procedure that involves tissue compression and application of heat such as the coaptic vessel closure has been automated. A MIMO nonlinear model characterizing the tissue stiffness and conductance under compression was feedback linearized and tuned PID controllers were used to control the system to achieve both the displacement and temperature constraints. A reference input for both the constraints were chosen as a ramp and hold trajectory which reflect the real constraints that exist in an actual surgical procedure. Our simulations showed that the controllers successfully tracked the reference trajectories with minimal deviation and in finite time horizon. The MIMO system with controllers developed in this work can be used to drive a surgical robot autonomously and perform electrosurgical procedures such as coaptic vessel closures.