  We introduced a non-symmetric tensor product of any two states or any two
representations of Cuntz-Krieger algebras associated with a certain
non-cocommutative comultiplication in previous our work. In this paper, we show
that a certain set of KMS states is closed with respect to the tensor product.
From this, we obtain formulae of tensor product of type {\rm III} factor
representations of Cuntz-Krieger algebras which is different from results of
the tensor product of factors of type {\rm III}.
