The need for efficient propulsion systems allied to increasingly more challenging fixed-wing UAV mission requirements has led to recent research on the autonomous thermal soaring field with promising results. As part of that effort, the feasibility and advantages of model predictive control (MPC)-based guidance and control algorithms capable of extracting energy from natural occurring updrafts have already been demonstrated numerically. However, given the nature of the dominant atmospheric phenomena and the amplitude of the required manoeuvres, a non-linear optimal control problem results. Depending on the adopted prediction horizon length, it may be of large order, leading to implementation and real-time operation difficulties. Knowing that, an alternative MPC-based autonomous thermal soaring controller is presented herein. It is designed to yield a simple and small non-linear programming problem to be solved online. In order to accomplish that, linear prediction schemes are employed to impose the differential constraints, thus no extra variables are added to the problem and only linear bound restrictions result. For capturing the governing non-linear effects during the climb phase, a simplified representation of the aircraft kinematics with quasi-steady corrections is used by the controller internal model. Flight simulation results using a 3 degree-of-freedom model subjected to a randomly generated time varying thermal environment show that the aircraft is able to locate and exploit updrafts, suggesting that the proposed algorithm is a feasible MPC strategy to be employed in a practical application.