Predicting the effect of climate change on biodiversity is a multifactorial problem that is complicated by potentially interactive effects with habitat properties and altered species interactions. In a microcosm experiment with communities of microalgae, we analysed whether the effect of rising temperature on diversity depended on the initial or the final temperature of the habitat, on the rate of change, on dispersal and on landscape heterogeneity. We also tested whether the response of species to temperature measured in monoculture allowed prediction of the composition of communities under rising temperature. We found that the final temperature of the habitat was the primary driver of diversity in our experimental communities. Species richness declined faster at higher temperatures. The negative effect of warming was not alleviated by a slower rate of warming or by dispersal among habitats and did not depend on the initial temperature. The response of evenness, however, did depend on the rate of change and on the initial temperature. Community composition was not predictable from monoculture assays, but higher fitness inequality (as seen by larger variance in growth rate among species in monoculture at higher temperatures) explained the faster loss of biodiversity with rising temperature.