  In this paper, we study the effect of $\kappa$-deformation of the space-time
on the response function of a uniformly accelerating detector coupled to a
scalar field. Starting with $\kappa$-deformed Klein-Gordon theory, which is
invariant under a $\kappa$-Poincar\'e algebra and written in commutative
space-time, we derive $\kappa$-deformed Wightman functions, valid up to second
order in the deformation parameter $a$. Using this, we show that the first
non-vanishing correction to the Unruh thermal distribution is only in the
second order in $a$. We also discuss various other possible sources of
$a$-dependent corrections to this thermal distribution.
