  We study the temperatures for the circular and drifted Rindler motions by
employing the Unruh-DeWitt detector method. In the circular motion, the
temperature is increasing along the radius of the circular motion until it
reaches the maximum, and then it is decreasing and eventually vanishing at the
limit to the radius where the proper acceleration is infinite. In fact, the
temperature is proportional to the proper acceleration quadratically near the
origin of the circular motion as compared to the usual Unruh effect depending
on the linear proper acceleration. On the other hand, in the drifted Rindler
motion, the observer moves with a relative velocity in the direction transverse
to the acceleration. If the detector is moving slowly in the transverse
direction with a finite proper acceleration, then the temperature behaves like
the usual Unruh temperature, while it vanishes for the speed of light in the
transverse direction according to the infinite proper acceleration.
Consequently, it turns out that the temperatures behave nonlinearly with
respect to the proper acceleration and the infinite proper acceleration would
not always permit the divergent temperature.
