Metal nanoparticles are important in several emerging technologies, but their size-selected thermodynamic properties are hard to obtain from experiment. We have characterized the energetic and structural properties of unsupported neutral Al-n (2 <= n < 65) particles (clusters and nanoparticles) via molecular dynamics quenching simulations with a recently validated many-body analytic potential. For each particle size (n), the global minimum-energy structure, the distribution of the local energy minima, and the finite-temperature thermodynamics have been calculated, the latter by evaluating similar to 100 000 rovibrational partition functions for the low-energy isomers of the various particles. This analysis demonstrates that the dominant structures of clusters and nanoparticles depend on temperature as well as particle size and that one must consider statistical mechanics as well as electronic structure in determining the dominant structures, stabilities, and properties of nanoparticles. As a particularly dramatic example, although the electronic magic numbers of Al-n are n = 13, 19, 23, 38, and 55 when thermal energy is neglected, the n = 38 magic number is found to become unstable relative to its neighbors (n = 37 and 39) at temperatures of 500 K and above due to vibrational energy and entropy effects. Furthermore, an energy-landscape analysis based on the probability of finding an isomer demonstrates that for many particle sizes, the global-minimum-energy structure on the potential energy surface is not the dominant structure at moderate temperatures, and other low-energy isomers may be dominant at temperatures as low as room temperature. For example, the four lowest-energy structures account for less than 50% of the population for n = 17, 31, 33, 34, 36, 37, 39, 41-43, 50, 56, 58, and 63-65 at 300 K and for n = 10, 11, and 17-65 at 1500 K. At 1500 K, even the 64 lowest-energy structures account for less than half the population for n = 23, 27-55, and 57-65. The increased importance of higher-energy structures at finite temperatures has important implications for understanding the size-selective reactivity and catalytic activity of metal nanoparticles. The isomeric energy (E-Iso), which is the difference between the thermal average energy of the particle and that of the corresponding global minimum structure in the ground electronic state, is introduced as an indicator of how well the thermochemical properties of a multi-isomer particle can be represented by those of the global minimum structure. Particularly low values for Al-12, Al-13, Al-19, Al-48, Al-53, Al-54, and Al-56 have been found in a wide temperature range.