  We have computed the black body radiation spectra in $\kappa-$Minkowski
space-time, using the quantum mechanical picture of massless scalar particles
as well as effective quantum field theory picture. The black body radiation
depends on how the field theory (and thus how the $\kappa-$Poincar\'e algebra)
handles the ordering effect of the noncommutative space-time. In addition,
there exists a natural momentum cut-off of the order $\kappa$, beyond which a
new real mode takes its shape from a complex mode and the old real mode flows
out to be a new complex mode. However, the new high momentum real mode should
not be physical since its contributions to the black-body radiation spoils the
commutative limit.
