Glycine on Cu(001) is used as an example to illustrate the critical role of molecular polarity and finite temperature effect in self-assembly of biomolecules at a metal surface. A unified picture for glycine self-assembly on Cu(001) is derived based on full polarity compensation considerations, implemented as a generic rule. Temperature plays a non-trivial role: the ground-state structure at 0 K is absent at room temperature, where intermolecular hydrogen bonding overweighs competing molecule-substrate interactions. The unique p(2X4) structure from the rule is proved as the most stable one by ab initio molecular dynamics at room temperature, and its STM images and anisotropic free-electron-like dispersion are in excellent agreement with experiments. Moreover, the rich self-assembling patterns including the heterochiral and homochiral phases, and their interrelationships are entirely governed by the same mechanism.