We measure the temperature-dependent carrier density and resistivity of the topological surface state of thin exfoliated Bi2Se3 in the absence of bulk conduction. When the gate-tuned chemical potential is near or below the Dirac point the carrier density is strongly temperature dependent reflecting thermal activation from the nearby bulk valence band, while above the Dirac point, unipolar n-type surface conduction is observed with negligible thermal activation of bulk carriers. In this regime linear resistivity vs. temperature reflects intrinsic electron-acoustic phonon scattering. Quantitative comparison with a theoretical transport calculation including both phonon and disorder effects gives the ratio of deformation potential to Fermi velocity D/hbarvF = 4.7 {AA}-1. This strong phonon scattering in the Bi2Se3 surface state gives intrinsic limits for the conductivity and charge carrier mobility at room temperature of ~550 {mu}S per surface and ~10,000 cm2/Vs.
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