Heat stress is poised to become a major factor negatively affecting plant performance worldwide. In terms of world food security, increased ambient temperatures are poised to reduce yields in cereals and other economically important crops. Grain amaranths are known to be productive under poor and/or unfavorable growing conditions that significantly affect cereals and other crops. Several physiological and biochemical attributes have been recognized to contribute to this favorable property, including a high water-use efficiency and the activation of a carbon starvation response. This study reports the behavior of the three grain amaranth species to two different stress conditions: short-term exposure to heat shock (HS) conditions using young plants kept in a conditioned growth chamber or long-term cultivation under severe heat stress in greenhouse conditions. The latter involved exposing grain amaranth plants to daylight temperatures that hovered around 50°C, or above, for at least 4 h during the day and to higher than normal nocturnal temperatures for a complete growth cycle in the summer of 2022 in central Mexico. All grain amaranth species showed a high tolerance to HS, demonstrated by a high percentage of recovery after their return to optimal growing conditions. The tolerance observed coincided with increased expression levels of unknown function genes previously shown to be induced by other (a)biotic stress conditions. Included among them were genes coding for RNA-binding and RNA-editing proteins, respectively. HS tolerance was also in accordance with favorable changes in several biochemical parameters usually induced in plants in response to abiotic stresses. Conversely, exposure to a prolonged severe heat stress seriously affected the vegetative and reproductive development of all three grain amaranth species, which yielded little or no seed. The latter data suggested that the usually stress-tolerant grain amaranths are unable to overcome severe heat stress-related damage leading to reproductive failure.