A strategy to mitigate the negative effects of stress on animals is to enhance their ability to beneficially respond to stressful conditions. This study aimed to assess whether prenatal ambient temperature influences the response of Japanese quail (Coturnix coturnix japonica) chicks to environmental challenges during growth. The experiment was conducted in a 2 × 2 factorial arrangement: two temperature conditions for the mothers (thermoneutral and heat stress by continuous exposure to 32 °C) and two offspring ambient temperature conditions (thermoneutral and heat stress by intermittent exposure to 34 °C for 6 h/day from 15 to 35 days of age). Heat stress in mothers led to lower laying rate, egg mass, expression of methionine sulfoxide reductase A (MSRA) gene, and antioxidant capacity as well as higher chick mortality rate (1–15 days of age). Maternal heat stress led to lower weight gain and total antioxidant capacity and higher feed conversion ratio. Maternal temperature × Offspring temperature interaction effects were observed on carbonylated protein content and HSP70, GSS, and MSRA gene expression. It was observed that, for chicks hatched from heat-stressed mothers, exposure to heat stress led to higher carbonylated protein content and HSP70 expression than exposure to thermoneutral conditions. Maternal heat stress was also responsible for increasing GSS expression in chicks grown under thermoneutral conditions. Chicks hatched from non-stressed mothers and subjected to heat stress had higher MSRA expression compared to chicks maintained in a thermoneutral environment. Our results show that, although maternal heat stress had no negative effects on performance or oxidative metabolism of offspring grown under thermoneutral conditions, it was associated with lower performance and higher protein oxidation in offspring exposed to heat stress during growth. These results could be due in part to alterations in the expression of genes related to antioxidant capacity.