In recent years, long periods of drought and heat waves have become increasingly frequent, causing forest dieback phenomena that make stands more sensitive to biotic stressors. How trees may respond to extreme climatic events and which metabolites are involved under stress conditions is still not clear. In this study, we analysed by SPME how dieback (D) and non-dieback (ND) Hungarian oak trees from the San Paolo Albanese site respond to these climatic dynamics, in terms of volatile organic compounds (VOCs). For each group of trees, three wood samples were taken, each divided into four sub-samples with 5 growth rings, subjected to SPME and increase in basal area (BAI) analysis of the last 20 years. Dieback trees had a lower amount of leaves, and this condition may translate into less photosynthesis, less organic matter production and lower reserves of carbohydrates available for growth. Indeed, D trees showed lower radial increases and a lower content of aldehydes, terpenes, and fatty acids than ND trees, indicating a better health of ND trees compared to D trees. While D trees showed a reduction in terpenes, such as α-pinene, γ-eudesmol, and cyperene (with significant insecticidal activity), a reduction in aromatic aldehydes, such as furfural and 5-methylfurfural, and an increase in silanols (with antimicrobial function). Considering the different compounds’ contents between D and ND trees, our study could be useful for detecting bio-indicators to identify an early warning signal of dieback phenomena.