Storage temperature is one of the most important factors affecting wine aging. Along with bottling parameters (type of stopper, SO2 level and dissolved O2 in wine), they determine how fast wine will evolve, reach its optimum and decline in sensory quality. At the same time, lowering of the SO2 level in wine has been a hot topic in recent years. In the current work, we investigated how Riesling wine evolved on the molecular level in warm (~25 °C) and cool (~15 °C) conditions depending on the SO2 level in the wine (low, medium and high), flushing of the bottle’s headspace with CO2 and three types of stoppers (Diam 30, Diam 30 origin and Diam 5) with different OIR levels (0.8–1.3 mg) and OTR levels (0.3–0.4 mg/year). It was demonstrated that the evolution of primary and secondary aromas, wine color and low molecular weight sulfur compounds (LMWSCs) during the two years of aging mainly depended on the storage temperature. Variation in the SO2 level and CO2 in the headspace affected mostly certain LMWSCs (H2S, MeSH) and β-damascenone. New aspects of C13-norisprenoids and monoterpenoids behavior in Riesling wine with different levels of SO2 and O2 were discussed. All three types of stoppers showed very close wine preservation properties during the two years of storage. The sensory analysis revealed that, after only six months, the warm stored wines with a low SO2 level were more oxidized and different from the samples with medium and high SO2 levels. A similar tendency was also observed for the cool stored samples.