Titanium diboride (TiB${}_2$) is a representative ultra-high-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 TiB${}_2$. We find that strong phonon-electron scattering suppresses the phonon thermal conductivity by nearly a factor of five 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 TiB${}_2$ and highlights the role of its topological multiband electronic structure in shaping anomalous thermal transport.