We study temperature-dependent hole transport in ideal crystal-phase poly(3-hexylthiophene) (P3HT) with ab initio calculations, with the aim of estimating the maximum mobility in the limit of perfect order. To this end, the molecular transfer integrals, phonon frequencies, and electron phonon coupling constants are obtained from density functional theory (DFT). This allows the determination of transport properties without fit parameters. The strong coupling between charge carriers and vibrations leads to strong scattering and polaronic effects that impact carrier transport. By providing an intrinsic mobility limit to ideal P3HT crystals, this work allows identification of the impact of disorder on the temperature-dependent transport in real samples. A detailed analysis of the transport-relevant phonon modes is provided that gives microscopic insight into the polaron effects and hints toward mobility optimization strategies.