Anomalous phonon thermal transport of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">He</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2

Previous research [Nat. Phys. 15, 1065 (2019)] has confirmed that helium can react with ice to form a superionic compound under extreme condition relevant to the ``hot ice'' layers of ice giants. While these findings reshape our understanding of these planetary materials, the thermal transport properties of such compounds, which are crucial parameter for modeling the dynamics and thermal history of these planets, remain uncharacterized. Here, we use first-principles calculations and the linearized phonon Boltzmann transport equation to systematically investigate the phonon dispersion, thermal conductivities, group velocities, phonon lifetimes, Gr"uneisen parameters, and mean free paths of ${\mathrm{He}}_{2}{\mathrm{H}}_{2}\mathrm{O}$ in both $I{4}_{1}md$ and $Fd\overline{3}m$ phases under high pressure conditions. Our results demonstrate marked differences in the transport dynamics of helium between ice VII and ice X sublattice attributed to the distinct strength and rigidity of hydrogen bonds. The room-temperature thermal conductivities of $I{4}_{1}md$ phase reach 16.4 W ${\text{m}}^{\ensuremath{-}1}$ ${\text{K}}^{--1}$ at 30 GPa and 27.9 W ${\text{m}}^{--1}$ ${\text{K}}^{--1}$ at 55 GPa, which are comparable to the experimental measurement of ice VII (\ensuremath{\sim}25 W ${\text{m}}^{-- }{\text{K}}^{--1}$ at 22 GPa), suggesting that the incorporation of interstitial He moderately suppresses the transport efficiency of phonon. However, the $Fd\overline{3}m$ phase exhibits dramatically reduced thermal conductivities of 1.4 W ${\text{m}}^{-- }{\text{K}}^{--1}$ at 60 GPa and 4.3 W ${\text{m}}^{-- }{\text{K}}^{--1}$ at 80 GPa, where optical phonons dominate the thermal transport with contributions exceeding 50%. These exceptional values mainly arise from synergistic effects of larger phonon group velocity, stronger anharmonicity, shorter phonon lifetime, and smaller mean free path. Such suppression of thermal conductivity in $Fd\overline{3}m\text{\ensuremath{-}}{\mathrm{He}}_{2}{\mathrm{H}}_{2}\mathrm{O}$ compound may alter conductivity distributions in the convective layer, inhibit helium-hydrogen demixing, and reduce heat transport efficiency, which may explain the multipolar magnetic field and anomalously low thermal flux observed in Uranus and Neptune. Our works elucidate the physical mechanism underlying the low thermal conductivity in the He-${\mathrm{H}}_{2}\mathrm{O}$ system under extreme conditions and provide critical insights into the dynamic process and thermal evolution of ice giants.