Agastache spp. are used as ornamental plants for their pleasant aroma and the different colors of flowers. Nowadays, their edible flowers have become attractive for their nutraceutical properties. Post-harvest treatment appears as a crucial point to avoid impairment of the nutraceutical compounds and aroma, so different treatments were tested to analyze their effect on the bioactive metabolites and volatilome. Results indicated that freeze-drying was the best solution to prolong the shelf life of these flowers. The use of high temperatures (50, 60, 70 °C) led to altered the composition of antioxidant compounds (phenolic compounds, flavonoids, anthocyanins, carotenoids). Air-drying at 30 °C was a reasonable method, even though time consuming. Concerning the aroma profile, all samples were dominated by oxygenated monoterpene compounds. Pulegone was the main or one of the major constituents of all samples together with p-menthone. Gas Chromatography-Mass Spectrometry results showed a correlation between the temperature and the number of identified compounds. Both fresh and freeze-dried samples evidenced a lesser number (10 and 19, respectively); when the temperature raised, the number of identified constituents increased. Statistical analyses highlighted significant differences between almost all aromatic compounds, even if both Principal Component and Hierarchical Cluster analyses differed at 60 and 70 °C and from the other treatments.