The structural, dynamical, and thermal properties of crystalline polyethylene are addressed with first-principles methods based on the density functional theory. The relatively low accuracy of the local density approximation for molecular crystals is corrected with the generalized gradient approximation, supplemented with empirical van der Waals' corrections, so as to optimize the description of the static (structural and elastic) properties of crystalline polyethylene. Based on this description, we perform first-principles finite temperature molecular dynamics simulations of warm, solid polyethylene. We analyze in particular thermal disorder effects, revealing the spontaneous appearance of trans-gauche defects close to the melting temperature (430 K).