  In the present paper we determine the radial part of the Casimir element for
the Lie algebra affine sl2 with respect to the Chevalley involution. The
resulting operator is identified with a blend of the Inozemtsev Hamiltonian and
the KZB-heat equation in dimension one. Moreover, it is shown how the
corresponding zonal spherical functions give rise to symmetric theta functions
and convergence is discussed. The paper takes guidance from previous work by
Etingof and Kirillov on the diagonal case.
