Peanuts are important oil crops and plant protein source. This study evaluated the influence of storage temperature (15, 25, and 35 °C) and time (0, 160, and 320 days) on the protein composition and the molecular structure of peanuts through sodium dodecyl sulfate polyacrylamide gel electrophoresis, particle size, total sulfhydryl (−SH) contents, nanostructural characterization, surface morphology microstructure, and spatial distribution of proteins and lipid analysis. Results showed that the basic subunits and disulfide contents of peanut protein were not affected by storage temperature and time. However, the −SH contents decreased significantly (P < 0.05) in all samples except the 15 °C/160 day storage group. The protein particle size and graininess increased when stored at 25 and 35 °C for 160 and 320 days, respectively; however, there was no significant change (P > 0.05) when stored at 15 °C. In addition, significant changes (P < 0.05) on the microscopic morphology and spatial distribution of protein and lipids were observed when stored at 25 and 35 °C for 320 days.