It is true. The tailllings question you can tell why nature works this way?
I try.
When you draw it in spacetime diagram you will see how it is works.
Whatever your speed is , the "lightspeed" related to you will be on lightcone always.
The two moving observers with +-0.5c have same lightcone...
There is no value of temperature in equation of time dilation.
The temperature may appear in this problem because the temperature can be tracked back to caotic motion.
But caotic motion means that there is no well defined direction of velocity.
Read carefull of words of Einstein.
All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)...
Yes the photon just a quanta of field. The field made of quantum harmonic oscillator.
The real problem here: QM say that the field is not element of reality.
Then element of what?
of a dream?