Drought and heat tolerance in plants is probably not a simply inherited single gene trait. Current thought is that while it is under genetic control there are probably many genes and gene products related to the character. Sorghum is quite tolerant of drought and the researchers at Texas A and M are using QTL Quantitative Trait Linkage to trace the keys to drought resistance in the plant. They have discovered that plants that do not breakdown rapidly at maturity the stay green trait are often better able to produce under drought conditions. The ability to maintain and not senescence seems to be associated with the ability to produce and maintain cytokinin production. Besides the genetic basis of drought tolerance the ability manage drought through agronomic practice should not be neglected. In major field crops the advancement in crop yield is associated about half to genetic improvement but the other half is related to agronomic practices. In reality the two need to combine to get the best results. When soil organic matter matter is optimized related to the farming system plants are able to respond to drought without the large losses experienced in impoverished soils.
To approach the genetics you find need to identify heat and drought tolerance/resistance by testing a wide range of genetic sources and then study their characteristics. These sources need to combined with appropriate commercial of end use backgrounds and than favor recombinations with both agronomics and defensive characters need be selected. The use of genomic analysis is very useful in this pursuit.
Since the crop of maize is so advanced it would good to look at the approaches the advanced workers have use. Gregory Edemeades is one of the foremost experts in the area.