The extreme and constant cold of the Southern Ocean has led to many unusual features of the Antarctic fauna. One of these, polar gigantism, is thought to have arisen from a combination of cold-driven low metabolic rates and high oxygen availability in the polar oceans (the ‘oxygen–temperature hypothesis'). If the oxygen–temperature hypothesis indeed underlies polar gigantism, then polar giants may be particularly susceptible to warming temperatures. We tested the effects of temperature on performance using two genera of giant Antarctic sea spiders (Pycnogonida), Colossendeis and Ammothea , across a range of body sizes. We tested performance at four temperatures spanning ambient (−1.8°C) to 9°C. Individuals from both genera were highly sensitive to elevated temperature, but we found no evidence that large-bodied pycnogonids were more affected by elevated temperatures than small individuals; thus, these results do not support the predictions of the oxygen–temperature hypothesis. When we compared two species, Colossendeis megalonyx and Ammothea glacialis , C. megalonyx maintained performance at considerably higher temperatures. Analysis of the cuticle showed that as body size increases, porosity increases as well, especially in C. megalonyx , which may compensate for the increasing metabolic demand and longer diffusion distances of larger animals by facilitating diffusive oxygen supply.