Tropical marine ecosystems are highly vulnerable to pollution and climate change. It is relatively unknown how tropical species may develop an increased tolerance to these stressors and the cost of adaptations. We addressed these issues by exposing a keystone tropical marine copepod, Pseudodiaptomus annandalei, to copper (Cu) for 7 generations (F1–F7) during three treatments: control, Cu and pCu (the recovery treatment). In F7, we tested the “contaminant-induced climate change sensitivity” hypothesis (TICS) by exposing copepods to Cu and extreme temperature. We tracked fitness and productivity of all generations. In F1, Cu did not affect survival and grazing but decreased nauplii production. In F2-F4, male survival, grazing, and nauplii production were lower in Cu, but recovered in pCu, indicating transgenerational plasticity. Strikingly, in F5-F6 nauplii production of Cu-exposed females increased, and did not recover in pCu. The earlier result suggests an increased Cu tolerance while the latter result revealed its cost. In F7, extreme temperature resulted in more pronounced reductions in grazing, and nauplii production of Cu or pCu than in control, supporting TICS. The results suggest that widespread pollution in tropical regions may result in high vulnerability of species in these regions to climate change.