Finite-temperature simulations of crystalline isotactic polypropylene are carried out self-consistently using a molecular mechanics force field for the interatomic potential and quasi-harmonic lattice dynamics for the vibrational free energy. Negative axial thermal expansion is observed, in agreement with experiment, and is attributed to elastic coupling to the transverse thermal stresses. The axial elastic modulus decreases with temperature, due to entropic effects and as a consequence of transverse thermal expansion, which acts to increase the unstrained volume and move the system to a region of the potential energy surface with lower curvature. The transverse and off-diagonal elastic moduli decrease with temperature, due to a decrease in the curvature of the potential energy surface as the chains move apart with thermal expansion.