Knowing in detail how the white and red wine aroma compounds behave under various storage conditions and especially at high temperature is important in order to understand the changes occurring to their sensorial character during the shelf life. The initial aim of this work was to develop and validate a fast, modern, robust, and comprehensive protocol for the quantification of 64 primary, secondary, and tertiary volatile compounds by using solid-phase extraction (SPE) cartridges in sample preparation and fast GC-MS/MS (gas chromatography-tandem mass spectrometry assay) in analysis. The protocol was applied to a study of the behavior of seven Gewürztraminer and seven Teroldego wines stored in anoxia at 50° C for 2.5 and 5 weeks. The results demonstrated a sharp decrease of the main linear terpenes linalool, geraniol, and nerol and the consequent increase of the cyclic ones, such as α-terpineol and 1,8-cineole; the increase of the C13-norisoprenoids 1,1,6,-trimethyl-1,2-dihydronapthalene (TDN), and β-damascenone and the C10 norisoprenoid safranal; the hydrolysis of acetates and linear esters; and the increase of some branched-chain esters. In red wines, a moderate increase was observed for some lactones. Some unwanted compounds, such as 2-aminoacetophenone (2-AAP), showed a notable increase in some Gewürztraminer wines, exceeding the olfactory threshold.