Brown macroalgae, particularly those from Fucus genus, are a rich and balanced source of bioactive nutrients and phytochemicals, such as dietary fibres (fucoidans, laminarins, and/or alginates), phlorotannins, and fucoxanthin, and some minerals, such as iodine, which have been demonstrated to possess numerous health-promoting properties. In fact, aqueous extracts of Fucus vesiculosus have been used as food supplements due to its rich content in bioactive compounds, though no study has been published on the optimization of this operation. Therefore, this study aimed to evaluate the impact of different extraction temperatures (25 °C, 50 °C, 75 °C, 100 °C, and 120 °C) and times (5 min, 1 h, 2 h, and 4 h) on the recovery of those bioactive compounds. The temperature was observed to positively influence the extraction of crude mass and of fucose polysaccharides only at 75 °C and above, and of iodine extraction at 50 °C and above. At these temperatures, time also showed to increase yields. Yields of crude extract, fucose, and iodine were successfully mathematically modelled with a power law, and its maximum yields were obtained at the highest temperature studied (120 °C) and longest extraction time (4 h). Iodine yield at these conditions provided extracts with relevant content to contribute to the recommended daily ingestion. Phlorotannins were significantly recovered at 120 °C though evidence of degradation was observed during time.