Room-temperature metallicity of lightly doped SrTiO$_3$ is puzzling, because the combination of mobility and the effective mass would imply a mean-free-path (mfp) below the Mott Ioffe Regel (MIR) limit and a scattering time shorter than the Planckian time ($tau_P=hbar/k_BT$). We present a study of electric resistivity, Seebeck coefficient and inelastic neutron scattering extended to very high temperatures, which deepens the puzzle. Metallic resistivity persists up to 900 K and is accompanied by a large Seebeck coefficient whose magnitude (as well as its temperature and doping dependence) indicates that carriers are becoming heavier with rising temperature. Combining this with neutron scattering data, we find that between 500 K and 900 K, the Bohr radius and the electron wave-length become comparable to each other and twice the lattice parameter. According to our results, between 100 K and 500 K, metallicity is partially driven by temperature-induced amplification of the carrier mass. We contrast this mass amplification of non-degenerate electrons with the better-known case of heavy degenerate electrons. Above 500 K, the mean-free-path continues to shrink with warming in spite of becoming shorter than both the interatomic distance and the thermal wavelength of the electrons. The latter saturates to twice the lattice parameter. Available theories of polaronic quasi-particles do not provide satisfactory explanation for our observations.
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