Sweetpotato, Ipomoea batatas (L.), a key food security crop, is negatively impacted by heat, drought, and salinity stress. The orange-fleshed sweetpotato cultivar “Beauregard” was exposed to heat, salt, and drought treatments for 24 and 48 h to identify genes responding to each stress condition in leaves. Analysis revealed both common (35 up regulated, 259 down regulated genes in the three stress conditions) and unique sets of up regulated (1337 genes by drought, 516 genes by heat, and 97 genes by salt stress) and down regulated (2445 genes by drought, 678 genes by heat, and 204 genes by salt stress) differentially expressed genes (DEGs) suggesting common, yet stress-specific transcriptional responses to these three abiotic stressors. Gene Ontology analysis of down regulated DEGs common to both heat and salt stress revealed enrichment of terms associated with “cell population proliferation” suggestive of an impact on the cell cycle by the two stress conditions. To identify shared and unique gene co-expression networks under multiple abiotic stress conditions, weighted gene co-expression network analysis was performed using gene expression profiles from heat, salt, and drought stress treated ‘Beauregard’ leaves yielding 18 co-expression modules. One module was enriched for “response to water deprivation,” “response to abscisic acid,” and “nitrate transport” indicating synergetic crosstalk between nitrogen, water, and phytohormones with genes encoding osmotin, cell expansion, and cell wall modification proteins present as key hub genes in this drought-associated module. This research lays the groundwork for exploring to a further degree, mechanisms for abiotic stress tolerance in sweetpotato.