Climate change, particularly ocean warming, is thought to benefit the spread of invasive species due to their increased tolerance to temperature fluctuations as compared to native species. The physiological tolerance of invasive species as a potential mechanism driving invasion success is therefore a subject that merits further study. Specifically, we need to adequately evaluate the potential of species invasions under changing environmental conditions, so that adequate preventive measures can be taken to minimize any impacts on coastal ecosystems. Here, we experimentally evaluated the physiological responses of a recent invader in the Southern Atlantic, the shrimp Lysmata lipkei, under a warming ocean scenario. Adult shrimps were collected from rocky shores in southeastern Brazil and subjected to experimental trials under a control and a + 3 °C scenario. Molecular biomarkers (in gills and muscle), upper thermal limits, acclimation response ratios, thermal safety margins, mortality rates, estimates of body condition and energy reserves were measured over 1 month. Results suggest that higher temperatures elicit physiological adjustments at the molecular level, underpinning a high thermal tolerance. In addition, results indicated substantial acclimation capacity, with no evidence of decreased performance under an ocean-warming scenario. Thermal safety margins were low for shrimp from intertidal rock pools but high for shrimp from subtidal habitats. We conclude that the thermal tolerance of this shrimp species may favor its ongoing invasion along the Southwestern Atlantic Ocean, mainly in subtidal habitats, both under present and future thermal conditions.