Loss of endosymbiotic algae (“bleaching”) under heat stress has become a major problem for reef-building corals worldwide. To identify genes that might be involved in triggering or executing bleaching, or in protecting corals from it, we used RNAseq to analyze gene-expression changes during heat stress in a coral relative, the sea anemone Aiptasia. We identified >500 genes that showed rapid and extensive up-regulation upon temperature increase. These genes fell into two clusters. In both clusters, most genes showed similar expression patterns in symbiotic and aposymbiotic anemones, suggesting that this early stress response is largely independent of the symbiosis. Cluster I was highly enriched for genes involved in innate immunity and apoptosis, and most transcript levels returned to baseline many hours before bleaching was first detected, raising doubts about their possible roles in this process. Cluster II was highly enriched for genes involved in protein folding, and most transcript levels returned more slowly to baseline, so that roles in either promoting or preventing bleaching seem plausible. Many of the genes in clusters I and II appear to be targets of the transcription factors NFκB and HSF1, respectively. We also examined the behavior of 337 genes whose much higher levels of expression in symbiotic than aposymbiotic anemones in the absence of stress suggest that they are important for the symbiosis. Unexpectedly, in many cases, these expression levels declined precipitously long before bleaching itself was evident, suggesting that loss of expression of symbiosis-supporting genes may be involved in triggering bleaching.