We have measured the ratio γ of the diffusion cross section to the angular momentum reorientation cross section in the colliding Fe-(^3)He and Ni-(^3)He systems. Nickel (Ni) and iron (Fe) atoms are introduced via laser ablation into a cryogenically cooled experimental cell containing cold (<1 K) (^3)He buffer gas. Elastic collisions rapidly cool the translational temperature of the ablated atoms to the (^3)He temperature. γ is extracted by measuring the decays of the atomic Zeeman sublevels. For our experimental conditions, thermal energy is comparable to the Zeeman splitting. As a result, thermal excitations between Zeeman sublevels significantly impact the observed decay. To determine γ accurately, we introduce a model of Zeeman state dynamics that includes thermal excitations. We find γ({Ni-^{3}He}=5×10^3) and γ({Fe-^{3}He}\leq3×10^3) at 0.75 K in a 0.8 T magnetic field. These measurements are interpreted in the context of submerged shell suppression of spin relaxation, as studied previously in transition metals and rare earth atoms.