Copper pollution can alter biological and trophic functions. Organisms can utilise different tolerance strategies, including accumulation mechanisms (intracellular vacuoles, external chelation, etc.) to maintain themselves in copper‐polluted environments. Accumulation mechanisms can influence the expression of other phenotypic traits, allowing organisms to deal with copper stress. Whether copper effects on accumulation strategies interact with other environmental stressors such as temperature and how this may differ within species are still unsolved questions. Here, we tested experimentally whether the combined effect of copper and temperature modulates traits linked to demography, morphology, movement and accumulation in six strains of the ciliate Tetrahymena thermophila. We also explored whether copper accumulation might modulate environmental copper concentration effects on phenotypic and demographic traits. Results showed high intraspecific variability in the phenotypic and demographic response to copper, with interactive effects between temperature and copper. In addition, they suggested an attenuation effect of copper accumulation on the sensitivity of traits to copper, but with great variation between strains, temperatures and copper concentrations. Diversity of responses among strains and their thermal dependencies pleads for the integration of intraspecific variability and multiple stressors approaches in ecotoxicological studies, thus improving the reliability of assessments of the effects of pollutants on biodiversity.