  A general consensus is--two causally disconnected Unruh-DeWitt detectors,
depending upon their motions, can be entangled through interaction with a
common background field. Here we investigate the effects of field temperature
$T^{(f)}$ on entanglement harvesting between two uniformly accelerated
detectors. In case of their parallel motion, the thermal nature of fields does
not produce any entanglement, and therefore, the outcome is the same as the
non-thermal situation. On the contrary, background temperature $T^{(f)}$ does
affect entanglement harvesting when the detectors are in anti-parallel motion,
i.e., one detector is in the right Rindler wedge (detector $A$), and the other
one is in the left Rindler wedge (detector $B$). While for $T^{(f)}=0$
entanglement harvesting is possible for all acceleration values $a_A$ of
detector $A$, in the presence of temperature, the situation is quite different.
In the latter case, entanglement harvesting is possible only within a narrow
range of $a_A$. For $(1+1)$ dimensions, the range starts from a certain value
and extends to infinity, and as we increase $T^{(f)}$, the required value of
$a_A$ for starting entanglement increases. Moreover, above a critical value,
$a_A=a_c$ harvesting increases as we increase $T^{(f)}$, which is just opposite
for accelerations below it. This feature does not change even if both the
detectors move with equal acceleration. In $(1+3)$ dimensions, we found many
critical values of $a_A$ when the detectors moved with different accelerations.
Besides, there exist several discrete ranges of $a_A$, contrary to the single
range in $(1+1)$ dimensions, for certain fixed values of $T^{(f)}$ within which
the entanglement harvesting is possible. Interestingly, for detectors moving
with equal acceleration, instead of multiple critical values, one has a single
critical point, with nature quite similar to $(1+1)$ dimensional results.
