  It has been predicted that an accelerating electron performs a Brownian
motion in the inertial frame. This Brownian motion in the inertial frame has
its roots in the interaction with the thermal excitation given by the Unruh
effect in the accelerating frame. If such a prediction is possible, we
correspondingly propose a prediction in this study that the thermal radiation
appears in the inertial frame from an electron heated by the Unruh effect in
the accelerating frame. The point in our prediction is, although the Unruh
effect is only in the accelerating frame, if the appearance of the Brownian
motion rooted in the Unruh effect in the inertial frame can be predicted, the
heat that the particle gets in its body by the Unruh effect in the accelerating
frame could survive in the inertial frame. Based on such a prediction, in this
paper we investigate phenomena in the neighborhood of an accelerating electron
in the inertial frame. The model we consider is the four-dimensional
Klein-Gordon real scalar field model with the Higgs type potential term at the
finite temperature identified with the Unruh temperature on the de Sitter
space-time. We calculate the one-loop effective potential in the inertial frame
with the corrections by the thermal radiation rooted in the Unruh effect in the
accelerating frame. In this calculation, we take into account that the
background space-time is deformed due to the field theory's corrected one-loop
effective potential. Based on such an analysis, we illustrate the restoration
of the spontaneous symmetry breaking and the variation of the background
space-time, and we examine the accelerating particle's world-line and the
amount of the energy corresponding to the change of the acceleration.
