Heat and drought are major stresses that significantly reduce seed yield of the common bean (Phaseolus vulgaris L.). In turn, this affects the profitability of the crop in climatic-vulnerable tropical arid regions, which happen to be the poorest and in most need of legume proteins. Therefore, it is imperative to broaden the sources of heat and drought resistance in the common bean by examining closely related species from warmer and drier environments (i.e., Tepary bean, P. acutifolius A. Gray), while harnessing such variation, typically polygenic, throughout advanced interspecific crossing schemes. As part of this study, interspecific congruity backcrosses for high temperature and drought tolerance conditions were characterized across four localities in coastal Colombia. Genotypes with high values of CO2 assimilation (>24 µmol CO2 m−2 s−1), promising yield scores (>19 g/plant), and high seed mineral content (Fe > 100 mg/kg) were identified at the warmest locality, Motilonia. At the driest locality, Caribia, one intercrossed genotype (i.e., 85) and the P. acutifolius G40001 control exhibited sufficient yield for commercial production (17.76 g/plant and 12.76 g/plant, respectively). Meanwhile, at southernmost Turipaná and Carmen de Bolívar localities, two clusters of genotypes exhibited high mean yield scores with 33.31 g/plant and 17.89 g/plant, respectively, and one genotype had an increased Fe content (109.7 mg/kg). Overall, a multi-environment AMMI analysis revealed that genotypes 13, 27, 82, and 84 were environmentally stable with higher yield scores compared to the Tepary control G40001. Ultimately, this study allows us to conclude that advanced common bean × Tepary bean interspecific congruity backcrosses are capable of pyramiding sufficient polygenic tolerance responses for the extreme weather conditions of coastal Colombia, which are likely to worsen due to climate change. Furthermore, some particular recombination events (i.e., genotype 68) show that there may be potential to couple breeding for heat and drought tolerance with Fe mineral biofortification, despite a prevalent trade-off, as a way to fight malnutrition of marginalized communities in tropical regions.