Heat and charge transport properties of the metallic unconventional clathrate BaNi2P4, hosting Ba cations in oversized Ni8P16 cages, are investigated. A novel method of single-crystal growth was developed, yielding 2–3 mm sized crystals of BaNi2P4. We also developed a setup to accurately measure thermal conductivity and electrical resistivity of the synthesized single crystals in a wide temperature range avoiding crystal remounting. BaNi2P4 has a metallic temperature dependence of its electrical resistivity (decreasing with decreasing temperature) and manifests an unconventional T2 power law for 50 K < T < 300 K; below 50 K, the power-law exponent increases gradually such that below 10 K the power law is T5, a predicted but extremely rarely experimentally observed dependence for peculiar electron–phonon interactions. Electronic band structure calculations, consistent with measurements of de Haas–van Alphen oscillations, show large band dispersions with significant contributions of Ba orbitals to states near the Fermi level, which is atypical for clathrates. The thermal properties of BaNi2P4 were probed using a combination of variable-temperature single-crystal X-ray diffraction experiments, heat capacity measurements, first-principles phonon dispersion calculations, and inelastic neutron scattering measurements. BaNi2P4 exhibits significant hybridization of the Ba-guest and Ni–P-framework vibrational modes, which may be enhanced via the detected split of the Ba position, which results in strong Ba-framework interactions.