The non-equilibrium dynamics of the kinetic spherical model with a non-conserved order-parameter, quenched to T≤T<Subscript>c</Subscript> from a fully disordered initial state, is studied at its upper critical dimension d=d<Superscript>*</Superscript>=4. In the scaling limit where both the waiting time s and the observation time t are large...</superscript></subscript>