We　theoretically　investigate　the　thermal-transport　properties　of　a　unitary　Fermi　gas　between　two　reservoirs　connected　by　a　quantum　point　contact.　We　find　several　distinguished　properties　that　are　qualitatively　different　from　those　of　weak　or　noninteracting　gas　systems.　The　particle　transport　figure　of　merit　is　drastically　enhanced　in　the　unitary　regime.　The　Lorentz　number　violates　the　Wiedemann-Franz　law,　demonstrating　the　breakdown　of　Fermi　liquid.　These　transport　properties　are　the　hallmarks　of　the　unitary　Fermi　gas　and　are　attributed　to　the　existence　of　preformed　Cooper　pairs.　The　variation　of　the　thermal-transport　coefficients　due　to　the　changing　of　the　transmission　coefficient　is　also　studied.