Heat stress has been a big challenge for animal survival and health due to global warming. However, the molecular processes driving heat stress response were unclear. In this study, we exposed the control group rats (n = 5) at 22 °C and the other three heat stress groups (five rats in each group) at 42 °C lasting 30, 60, and 120 min, separately. We performed RNA sequencing in the adrenal glands and liver and detected the levels of hormones related to heat stress in the adrenal gland, liver, and blood tissues. Weighted gene co-expression network analysis (WGCNA) was also performed. Results showed that rectal temperature and adrenal corticosterone levels were significantly negatively related to genes in the black module, which was significantly enriched in thermogenesis and RNA metabolism. The genes in the green-yellow module were strongly positively associated with rectal temperature and dopamine, norepinephrine, epinephrine, and corticosterone levels in the adrenal glands and were enriched in transcriptional regulatory activities under stress. Finally, 17 and 13 key genes in the black and green-yellow modules were identified, respectively, and shared common patterns of changes. Methyltransferase 3 (Mettl3), poly(ADP-ribose) polymerase 2 (Parp2), and zinc finger protein 36-like 1 (Zfp36l1) occupied pivotal positions in the protein–protein interaction network and were involved in a number of heat stress-related processes. Therefore, Parp2, Mettl3, and Zfp36l1 could be considered candidate genes for heat stress regulation. Our findings shed new light on the molecular processes underpinning heat stress.