The temperature dependence of the irreversible phase transition from a two-dimensional gas to an ordered zero-dimensional solid on the Si(111)-7 × 7 surface was studied using photoemission spectroscopy. With increasing Na coverage, the two-dimensional Na gas, which is a state of highly mobile Na atoms, undergoes a phase transition into ordered zero-dimensional magic nanoclusters at room temperature. The critical Na coverage of the phase transition was found to increase with reduced temperature. This was used to develop a gas-solid phase diagram of Na atoms on the Si(111)-7 × 7 surface as a function of Na coverage and sample temperature based on the electronic structure. The temperature dependence of the phase transition can be ascribed to the suppression of the thermal energy that is required to overcome the energetic barrier between the two-dimensional gas and the zero-dimensional solid at low temperature, where three different hopping mechanisms are related to the phase transition.