To realize magnonic devices, finding a way to make magnons better transport and efficiently pump their spin angular momentum across a ferromagnetic insulator (FMI)/normal metal (NM) interface is crucial. Here, demonstrate that modulating magnon temperature in an FMI offers an effective way to manipulate magnon transport and can lead to significantly enhanced spin pumping when the process is driven by a temperature gradient. This modulation is achieved by engineering the interface between the substrate and the FMI in substrate/FMI/NM heterostructure, such that the interface provides stronger energy exchange between phonons in the substrate and magnons in the FMI. We report a 265% enhanced spin Seebeck effect, which represents the thermally driven spin-pumping process, and a 122% enhanced magnon current density participating in the spin pumping. Theoretical and experimental evidence coherently indicate that the observed enhancement should be attributed to the modified magnon temperature profile in the FMI.