The responses of lowland tropical communities to climate change will critically influence global biodiversity but remain poorly understood. If species in these systems are unable to tolerate warming, the communities—currently the most diverse on Earth—may become depauperate (‘biotic attrition’). In response to temperature changes, animals can adjust their distribution in space or their activity in time, but these two components of the niche are seldom considered together. We assessed the spatio-temporal niches of rainforest mammal species in Borneo across gradients in elevation and temperature. Most species are not predicted to experience changes in spatio-temporal niche availability, even under pessimistic warming scenarios. Responses to temperature are not predictable by phylogeny but do appear to be trait-based, being much more variable in smaller-bodied taxa. General circulation models and weather station data suggest unprecedentedly high midday temperatures later in the century; predicted responses to this warming among small-bodied species range from 9% losses to 6% gains in spatio-temporal niche availability, while larger species have close to 0% predicted change. Body mass may therefore be a key ecological trait influencing the identity of climate change winners and losers. Mammal species composition will probably change in some areas as temperatures rise, but full-scale biotic attrition this century appears unlikely.