I transport my snakes in a snake bag or pillowcase, and then in a rubbermaid container. For short trips I don't bother with heat. But if its a longer trip I will bring an extra heat pad and thermostat. If there are no outlets where I am going I will bring an instant heat pack thing.
You can kinda tell when they start to get stressed. their movements are more like them trying to get away than them just casually checking things out.
Ball pythons are pretty chill snakes. They are generally good around new people but any new situation is going to be stressful to your animal. It is wise to limit handling and to limit the number of people to keep stress levels low. If you notice your animal getting stressed, it is probably time to give them some alone time.