  We analyze the response of a detector with a uniform acceleration $\alpha$ in
$\kappa-$Minkowski spacetime using the first order perturbation theory. The
monopole detector is coupled to a massless complex scalar field in such a way
that it is sensitive to the Lorentz violation due to the noncommutativity of
spacetime present in the $\kappa-$deformation. The response function deviates
from the thermal distribution of Unruh temperature at the order of $1/\kappa$
and vanishes exponentially as the proper time of the detector exceeds a certain
critical time, a logarithmic function of $\kappa$. This suggests that the Unruh
temperature becomes not only fuzzy but also eventually decreases to zero in
this model.
