Due to high perishability, plums are harvested at an early stage of maturity to extend postharvest storage life. Storage time and temperature can significantly affect the phytochemical and sugar composition of plums, altering their palatability and nutritional quality. In this study, variations in physiochemical properties (total soluble solids (TSS), titratable acidity (TA), color (chroma and hue angle)), phytochemical composition (total phenolic content (TPC), total anthocyanin content (TAC), and carotenoids), and sugars in three different tissues of the Queen Garnet plum (QGP) during storage at two common domestic storage temperatures (4 and 23 °C) were evaluated. There was an increase (p > 0.05) in TSS and a reduction (p < 0.05) in TA of the outer flesh at 23 °C. Chroma values of all the tissues reduced (p < 0.05) at 23 °C. At 4 °C, chroma values fluctuated between storage days. The TAC of the peel was the highest (p < 0.05) among the different tissues and continued to increase up to 10 days of storage at 23 °C (3-fold increase). At 4 °C, the highest (p < 0.05) TAC (peel) was observed after 14 days of storage (1.2-fold increase). TPC showed similar results. The highest (p < 0.05) TPC was recorded in the peel after 10 days of storage at 23 °C (2.3-fold increase) and after 14 days of storage at 4 °C (1.3-fold increase), respectively. Total carotenoids in the flesh samples at both storage temperatures were reduced (p < 0.05) after 14 days. Total sugars also decreased during storage. The results of the present study clearly showed that common domestic storage conditions can improve the nutritional quality of plums by increasing the content of bioactive anthocyanins and other phenolic compounds. However, the increase in phytochemicals needs to be counterbalanced with the decrease in total sugars and TA potentially affecting the sensory attributes of the plums.