  Considering two accelerated observers with same acceleration in two timelike
wedges of Rindler frame we calculate the Feynman-{\it like} propagators for a
real scalar field in a thermal bath with respect to the Minkowski vacuum. Only
the same wedge correlators are symmetric under the exchange of the {\it real}
thermal bath and Unruh thermal bath, while the cross-wedge ones are not.
Interestingly, they contain a cross term which is a collective effects of
acceleration and thermal nature of field. Particularly the zero temperature
description along with {\it no analytic continuation} between coordinates in
right and left Rindler wedges, as expected, corresponds to usual
thermofield-double formalism. However, unlike in later formulation, the two
fields are now parts of the original system. Moreover it bears the features of
a spacial case of closed-time formalism (CTP) where the Keldysh contour is
along the increasing Rindler time in the respective Rindler wedges.
Interestingly, we observe a new feature that the analytic continuation between
the wedges provides the two more spacial cases of CTP. Hence
Rindler-frame-field theory seems to be a viable candidate to deal thermal
theory of fields and may illuminate the search for a bridge between the usual
existing formalisms.
