Amorphous hafnia (a-HfO₂) has attracted considerable attention due to its excellent dielectric properties and broad applicability in the electronic industry. Considering that the self-heating is becoming the bottleneck for the performance and reliability of microelectronic devices, it is necessary to clarify the thermal transport mechanism in a-HfO₂. The microstructures of a-HfO₂ can be significantly changed during the fabrication process, whose effects on thermal transport remain to be revealed. Here, we conduct a comprehensive investigation of thermal transport in a-HfO₂ based on the quasi-harmonic Green-Kubo (QHGK) theory combined with hydrodynamic extrapolation. The calculation scheme fully considers the contributions from low-frequency vibrational modes, overcoming the drawbacks of finite size in the single QHGK method and molecular dynamics simulation. It is found that the thermal conductivity (κ) of a-HfO₂ is weakly related to its degree of order. The amorphous structures with slower quenching speed and higher degree of order have higher thermal conductivities due to their slightly larger relaxation times. Modal analyses show that the mid- and low-frequency vibrational modes have significant contributions to thermal transport in a-HfO₂, which is the main reason for the underestimation of the κ in other methods. Based on the anharmonic dynamic structure factor, we further separate the contributions of two fundamental heat carriers in amorphous materials: propagons and diffusons. It is found that diffusons dominate the κ in all a-HfO₂ structures. Nevertheless, the contribution of the propagons is non-negligible, accounting for more than 20% and increasing with the degree of structural ordering. This study provides new insights into the microscopic mechanisms and guidance for manipulating thermal transport in a-HfO₂.