  The main purpose of this paper is to identify the tempered modules for the
affine Hecke algebra of type $C_n^{(1)}$ with arbitrary, non-root of unity,
unequal parameters, in the exotic Deligne-Langlands correspondence in the sense
of Kato. Our classification has several applications to the Weyl group module
structure of the tempered Hecke algebra modules. In particular, we provide a
geometric and a combinatorial classification of discrete series which contain
the sign representation of the Weyl group. This last combinatorial
classification was expected from the work of Heckman-Opdam and Slooten.
