To achieve an excellent automobile transmission shaft with good thermal stability, the following key factors need to be considered:

1. Material selection: The transmission shaft is usually made of high-temperature alloy steel or other high-temperature resistant materials to ensure that it is not easy to deform or fail at high temperature.

2. Surface treatment: The surface of the transmission shaft is usually treated with special heat treatment or coating to enhance its surface hardness and wear resistance and improve its high temperature resistance. 

3. Structural design: The structural design of the transmission shaft needs to consider the working conditions in high temperature environment, and reasonably design the structural form and size of the transmission shaft to ensure the stability and reliability of the transmission shaft in high temperature. 

4. Cooling system: In some high-performance vehicles or high-load working conditions, we can consider setting a cooling system around the transmission shaft to reduce the working temperature of the transmission shaft by circulating cooling medium and improve its thermal stability and high-temperature resistance.

5. Quality control: In the production process of transmission shaft, it is necessary to strictly control the material selection, processing technology and assembly process to ensure the quality stability and consistency of transmission shaft, so as to improve its thermal stability and reliability.