Quinoa (Chenopodium quinoa Willd.) is a highly nutritious crop that is resilient to a wide range of abiotic stresses; however, sensitivity to high temperatures is regarded as an impediment to adoption in regions prone to heat waves. Heat stress is usually associated with a decrease in crop reproductive capacity (e.g., pollen viability), yet little is known about how leaf physiological performance of quinoa is affected by high temperatures. Several trials were conducted to understand the effect of high temperatures, without confounding stressors such as drought, on ten selected quinoa genotypes considered to encompass heat sensitive and heat tolerant plant material. Plants were grown under favorable temperatures and exposed to two temperature treatments over four consecutive days. The heat treatment simulated heat waves with maximum and minimum temperatures higher during the day and night, while the control treatment was maintained under favorable temperatures (maximum and minimum temperatures for ‘Heat’: 45/30 °C and ‘Control’: 20/14 °C). Leaf gas exchange (day), chlorophyll fluorescence (predawn and day) and dark respiration (night) were measured. Results show that most quinoa genotypes under the heat treatment increased their photosynthetic rates and stomatal conductance, resulting in a lower intrinsic water use efficiency. This was partly corroborated by an increase in the maximum quantum yield of photosystem II (Fv/Fm). Dark respiration decreased under the heat treatment in most genotypes, and temperature treatment did not affect aboveground biomass by harvest (shoot and seeds). These results suggest that heat stress alone favors increases in leaf carbon assimilation capacity although the tradeoff is higher plant water demand, which may lead to plant water stress and lower yields under non-irrigated field conditions.