In micro-LED chip repair, a nanopositioner is commonly used to adjust the positioning of the LED chip. However, during the bonding process, the heat generated can cause the positioning system to deform, leading to inaccurate alignment and poor-quality chip repair. To solve this issue, a novel flexible connection structure has been proposed that can eliminate thermal deformation. The principle of this novel flexible connection structure is that the thermal distortion self-elimination performance is achieved via three flexible connection modules (FCM) so that the thermal stress is automatically eliminated. First, the paper introduces the principle of thermal deformation elimination, and then the design and modeling process of the proposed structure are described. A heat transfer model is then developed to determine how temperature is distributed within the structure. A thermal deformation model is established, and the size of the FCM is optimized using a genetic algorithm (GA) to minimize the thermal deformation. Finite element analysis (FEA) is used to simulate and evaluate the thermal distortion self-elimination performance of the optimized mechanism. Finally, experiments are conducted to verify the reliability and accuracy of the simulation results. The simulations and experiments show that the proposed structure can eliminate more than 38% of the thermal deformation, indicating an excellent thermal deformation self-eliminating capability.