In Drosophila, just as in vertebrates, changes in external temperature are encoded by bidirectional opponent thermoreceptor cells: some cells are excited by warming and inhibited by cooling, whereas others are excited by cooling and inhibited by warming. The central circuits that process these signals are not understood. In Drosophila, a specific brain region receives input from thermoreceptor cells. Here we show that distinct genetically identified projection neurons (PNs) in this brain region are excited by cooling, warming, or both. The PNs excited by cooling receive mainly feed-forward excitation from cool thermoreceptors. In contrast, the PNs excited by warming ('warm-PNs') receive both excitation from warm thermoreceptors and crossover inhibition from cool thermoreceptors through inhibitory interneurons. Notably, this crossover inhibition elicits warming-evoked excitation, because warming suppresses tonic activity in cool thermoreceptors. This in turn disinhibits warm-PNs and sums with feed-forward excitation evoked by warming. Crossover inhibition could cancel non-thermal activity (noise) that is positively correlated among warm and cool thermoreceptor cells, while reinforcing thermal activity which is anti-correlated. Our results show how central circuits can combine signals from bidirectional opponent neurons to construct sensitive and robust neural codes.