Climate change causes shifts in temperature patterns, and plants adapt their chemical content in order to survive. We compared the effect of low (LT) and high (HT) growing temperatures on the phytochemical content of broccoli (Brassica oleracea L. convar. botrytis (L.) Alef. var. cymosa Duch.) microgreens and the bioactivity of their extracts. Using different spectrophotometric, LC-MS/MS, GC-MS, and statistical methods, we found that LT increased the total phenolics and tannins in broccoli. The total glucosinolates were also increased by LT; however, they were decreased by HT. Soluble sugars, known osmoprotectants, were increased by both types of stress, considerably more by HT than LT, suggesting that HT causes a more intense osmotic imbalance. Both temperatures were detrimental for chlorophyll, with HT being more impactful than LT. HT increased hormone indole-3-acetic acid, implying an important role in broccoli’s defense. Ferulic and sinapic acid showed a trade-off scheme: HT increased ferulic while LT increased sinapic acid. Both stresses decreased the potential of broccoli to act against H2O2 damage in mouse embryonal fibroblasts (MEF), human keratinocytes, and liver cancer cells. Among the tested cell types treated by H2O2, the most significant reduction in ROS (36.61%) was recorded in MEF cells treated with RT extracts. The potential of broccoli extracts to inhibit α-amylase increased following both temperature stresses; however, the inhibition of pancreatic lipase was increased by LT only. From the perspective of nutritional value, and based on the obtained results, we conclude that LT conditions result in more nutritious broccoli microgreens than HT.