The temperature dependence of the stability of infinite poly-L-alanine (x, T, and 310 helices with respect to the fully extended structure (FES) is calculated using density functional theory and the harmonic approximation. We find that the vibrational entropy strongly reduces the stability of the helical conformations with respect to the FES. By mapping the ab initio data on an approximate mechanical model, we show that this effect is exclusively due to the formation of hydrogen bonds, whereas changes in the backbone stiffness are practically negligible. We furthermore observe that the temperature dependence is largest for the pi helix and smallest for the 3(10) helix and demonstrate that these trends are a generic behavior related to the geometric peculiarities of the respective helical conformations and independent of the specific amino acid sequence.