Increasing global temperatures and a growing world population create the need to develop crop varieties that provide higher yields in warmer climates. There is growing interest in expanding quinoa cultivation, because of the ability of quinoa to produce nutritious grain in poor soils, with little water and at high salinity. The main limitation to expanding quinoa cultivation, however, is the susceptibility of quinoa to temperatures above approximately 32°C. This study investigates the phenotypes, genes and mechanisms that may affect quinoa seed yield at high temperatures. Using a differential heating system where only roots or only shoots were heated, quinoa yield losses were attributed to shoot heating. Plants with heated shoots lost 60-85% yield as compared with control plants. Yield losses were the result of lower fruit production, which lowered the number of seeds produced per plant. Furthermore, plants with heated shoots had delayed maturity and greater non-reproductive shoot biomass, whereas plants with both heated roots and heated shoots produced higher yields from the panicles that had escaped the heat, compared with the control. This suggests that quinoa uses a type of avoidance strategy to survive heat. Gene expression analysis identified transcription factors differentially expressed in plants with heated shoots and low yield that had been previously associated with flower development and flower opening. Interestingly, in plants with heated shoots, flowers stayed closed during the day while the control flowers were open. Although a closed flower may protect the floral structures, this could also cause yield losses by limiting pollen dispersal, which is necessary to produce fruit in the mostly female flowers of quinoa.