  The Unruh effect refers to the thermal fluctuations a detector experiences
while undergoing linear motion with uniform acceleration in a Minkowski vacuum.
This thermality can be demonstrated by tracing the vacuum state of the field
over the modes beyond the accelerated detector's event horizon. However, the
event horizon is well-defined only if the detector moves with eternal uniform
linear acceleration. This idealized condition cannot be fulfilled in realistic
situations when the motion unavoidably involves periods of non-uniform
acceleration. Many experimental proposals to test the Unruh effect are of this
nature. Often circular or oscillatory motion, which lacks an obvious geometric
description, is considered in such proposals. The proper perspective for
theoretically going beyond, or experimentally testing, the Unruh-Hawking effect
in these more general conditions has to be offered by concepts and techniques
in non-equilibrium quantum field theory. In this paper we provide a detailed
analysis of how an Unruh-DeWitt detector undergoing oscillatory motion responds
to the fluctuations of a quantum field. Numerical results for the late-time
temperatures of the oscillating detector are presented. We comment on the
digressions of these results from what one would obtain from a naive
application of Unruh's result.
