This study was carried out in the private farm in Tahta city, Sohag, Egypt, during the four successive seasons, i.e., 2016/2017 2017/2018, 2018/2019 and 2019/2020 to estimate observed and expected responses to selection and other genetic parameters for a bread wheat population (Debeira × Sakha 8) in F2, F3, F4 and F5 generations under timely and late planting (heat stress). The results showed that observed direct response to selection for grain yield in F4 and F5 generations resulted in significant positive observed gain compared with bulk, better parent and the check cv (Sids 12) under the two conditions. On the other hand, the expected responses to selection were 6.89 and 11.60 % in F4 generation and were 2.36 and 4.60 % in F5 generation under timely and heat stress, respectively. The narrow sense heritability was 55.02, 44.50 and 27.83 % in F3, F4 and F5 generations under timely conditions, respectively. Meanwhile, they were 55.44, 57.05 and 24.68 % in the same generations under heat stress. These results showed that the pedigree method of selection was effective to produce new tolerant lines to heat stress with high grain yield. Depending on Drought Susceptibility Index, the two lines, i.e., no. 453 and 459 in F4 and F5 generations produced relatively high grain yield under heat stress due to high yield potential, rather than having low susceptibility to stress. These lines could be used as source of heat tolerance/or factors contributing to general adaptation.