A universal coordinate transformation leading to Hawking effect is obtained from only a few conditions whose physical meaning is clear. It is pointed out that the separation of the time variable and the space variable in the coordinate transformation is a sufficient condition for introducing the thermal effect when the new space-time is stationary and time-orthogonal. It is inferred that the "separation" in the coordinate transformation may be regarded as a new representation of the fundamental postulate upon which statistical mechanics is built.