Chloroplasts’ mechanisms of adaptation to elevated temperatures are largely determined by the gene expression of the plastid transcription apparatus. Gene disruption of iron-containing superoxide dismutase PAP4/FSD3 and PAP9/FSD2, which are parts of the DNA–RNA polymerase complex of plastids, contributed to a decrease in resistance to oxidative stress caused by the prolonged action of elevated temperatures (5 days, 30 °C). Under heat stress conditions, pap4/fsd3 and pap9/fsd2 mutants showed a decline in chlorophyll content and photosynthesis level, as measured by photosynthetic parameters, and a different amplitude of HSP gene response to heat stress. The expression of nuclear- and plastid-encoded photosynthesis genes and corresponding proteins was strongly inhibited in the mutants as compared with wild-type plants and was further suppressed or displayed no additional changes at 30 °C. NEP-dependent plastid genes, as well as NEP genes RPOTp and RPOTmp, were also downregulated in the mutants by high temperature or remained stable, unlike in wild-type seedlings where these genes were strongly upregulated. The results obtained correspond to the concept of the complex effect of various forms of reactive oxygen species under all types of stresses, including heat stress, and confirm the hypothesis of a new regulatory function in plastid transcription acquired by enzymatic proteins during evolution.