There has been an explosion of recent evidence that environments experienced by fathers or their ejaculates can influence offspring phenotypes (paternal effects). However, little is known about whether such effects are adaptive, which would have far-reaching implications for the many species facing rapidly changing environments. For example, some arguments suggest paternal effects might be a source of cross-generational plasticity, preparing offspring to face similar conditions to their father (anticipatory hypothesis). Alternatively, ejaculate-mediated effects on offspring may be non-adaptive by-products of stress. Here, we conduct an experiment to distinguish between these predictions, exposing ejaculates of the externally fertilizing mussel Mytilus galloprovincialis to ambient (19 degrees C) and high (24 degrees C) temperatures, then rearing offspring groups in temperatures that match and mismatch those of sperm. We find that, overall, high temperature-treated sperm induced higher rates of normal offspring development and higher success in transitioning to second-stage larvae, which may represent adaptive epigenetic changes or selection on sperm haplotypes. However, the progeny of high temperature-treated sperm did not perform better than those of ambient temperature-treated sperm when rearing temperatures were high. Overall, these findings offer little support for the anticipatory hypothesis and suggest instead that beneficial paternal effects may be eroded when offspring develop under stressful conditions.