The pyrochlore material Yb₂Ti₂O₇ displays unexpected quasi-two-dimensional (2D) magnetic correlations within a cubic lattice environment at low temperatures, before entering an exotic disordered ground state below T = 265 mK. We report neutron scattering measurements of the thermal evolution of the 2D spin correlations in space and time. Short-range three-dimensional (3D) spin correlations develop below 400 mK, accompanied by a suppression in the quasielastic (QE) scattering below ∼0.2 meV. These show a slowly fluctuating ground state with spins correlated over short distances within a kagome-triangular-kagome (KTK) stack along [111], which evolves to isolated kagome spin stars at higher temperatures. Furthermore, low-temperature specific heat results indicate a sample dependence to the putative transition temperature that is bounded by 265 mK, which we discuss in the context of recent mean field theoretical analysis.