The question is somewhat mixed so I will try to restate it as I understood it and you should correct me if I got it wrong.
As I see, the question here is: why does a thin film of liquid crystals changes its color as it gets colder or warmer?.
The answer to this question is interference. The light is reflected from both the top and the bottom surface of the film and the two reflections will interfere with each other. If for some wavelength accumulated phase difference between reflections is close to a multiple of $2\pi$ then the interference is constructive and this color will be enhanced in reflecting light.
The phase difference difference depends on the path length, and when the film gets thicker, the wavelength of reflected light will shift towards red.