We present theoretical calculations of thermally averaged elastic cross sections and spin-relaxation rate coefficients in the temperature range 0.1 to 300 mK for magnetically trapped, doubly polarized cesium atoms. The calculations reproduce the recent experimental results of Arndt et al. (1997) and Soding et al. (1998) for cases where the aSu ground state potential of Cs2 possesses a large scattering length (jA3j . 35 nm) and the magnitude of the second-order spin-orbit interaction is scaled to reproduce room temperature scattering data. [S0031-9007(98)06865-3]