With the intensive development of the sheep industry and increasing global temperatures, heat stress in sheep has become an increasingly severe and important issue in recent years. The level of N6-methyladenosine (m6A) RNA methylation changes in response to stress plays important roles in stress responses. However, the role of m6A in the heat stress response of sheep remains unclear. To explore this issue, we measured heat stress protein (HSP) expression, liver function indexes, m6A on RNA, m6A-related enzyme expression, and tissue damage in sheep that had been subjected to heat stress. At the transcriptome level, our results showed significant increases in m6A on RNA and increased mRNA levels of HSPs (HSP70, HSP90, and HSP110) and m6A-related enzymes [METTL3 (methyltransferase-like 3), METTL14 (methyltransferase-like 14), WTAP (wilms tumor 1-associated protein), FTO (fat mass and obesity-associated protein), ALKBH5 (alkB homologue 5), YTHDF1-3 (YTH domain family proteins), and YTHDC1-2 (YTH domain-containing proteins)] following heat stress. At the protein level, the expression of METTL3, YTHDF1-2, and YTHDC2 showed no significant differences following heat stress. However, in contrast to its mRNA level after heat stress, the protein expression of YTHDF3 was reduced, while the expression of HSPs (HSP70, HSP90, and HSP110), METTL14, WTAP, FTO, ALKBH5, YTHDF3, and YTHDC1 increased in line with their measured mRNA levels. Histological experiments revealed that heat stress caused varying degrees of damage to sheep liver tissue. Moreover, immunohistochemical staining indicated that the m6A-related enzymes were expressed in sheep hepatocytes, and differences in expression patterns were observed between the control and heat stress groups. In summary, differences in the level of m6A and the expression of m6A-related enzymes in the liver of sheep were observed after heat stress. This indicates that m6A is involved in the regulation of heat stress in sheep. Our findings provide a new avenue for studying the responses to heat stress in sheep.