An important question in the physics of superconducting nanostructures is the role of thermal fluctuations (TFs) on superconductivity in the zero-dimensional limit. Here, we probe the evolution of superconductivity as a function of temperature and particle size in single, isolated Pb nanoparticles. Accurate determination of the size and shape of each nanoparticle makes our system a good model to quantitatively compare the experimental findings with theoretical predictions. In particular we study the role of TFs on the tunneling density of states (DOS) and the superconducting energy gap (Delta) in these nanoparticles. For the smallest particles h <= 13 nm, we clearly observe a finite energy gap beyond T-c giving rise to a "critical region." We show explicitly through quantitative theoretical calculations that these deviations from mean-field predictions are caused by TFs. Moreover, for T << T-c, where TFs are negligible and typical sizes below 20 nm, we show that Delta gradually decreases with reduction in particle size. This result is described by a theoretical model that includes finite size effects and zero temperature leading order corrections to the mean-field formalism.