Titanium diboride (${\mathrm{TiB}}_2$) is a representative ultrahigh-temperature ceramic and topological semimetal with exceptional mechanical and thermal properties. However, a comprehensive understanding of its intrinsic thermal transport mechanisms remains lacking. Here, we present a systematic first-principles investigation of the coupled electron and phonon thermal transport in ${\mathrm{TiB}}_2$. We find that strong phonon-electron scattering suppresses the phonon thermal conductivity by nearly a factor of 5 even at room temperature, resulting in an unusually weak temperature ($T$) dependence rather than the conventional $T^{-1}$ behavior. In contrast to common metals, the electronic thermal conductivity increases monotonically even in the high-temperature regime, driven by the anomalous energy dependence of the carrier lifetime associated with a pronounced dip in the electronic density of states near the Fermi level. Moreover, the symmetry-protected topological band crossings near the Fermi energy promote substantial electron-hole compensation, which enhances the electronic thermal conductivity and drives the Lorenz number above the Sommerfeld value. Our work establishes a unified picture of heat conduction in ${\mathrm{TiB}}_2$ and highlights the role of its topological multiband electronic structure in shaping anomalous thermal transport.

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• Electrical conductivity
• Electron-phonon coupling
• Thermal conductivity
• Topological materials
• Density functional theory
• First-principles calculations