A total of 288 1-day-old Ross 308 broiler chicks were randomly allotted into four dietary treatments: (1) Control (CON; corn–wheat–soybean-based diet), (2) CON + 0.05% bacitracin methylene disalicylate (BMD), (3) CON + 0.3% red osier dogwood extract (ROD), and (4) CON + 2.5% grape pomace (GP) and raised for 28 days. On days 21–27, birds were exposed to either a thermoneutral (TN; 24 ± 1 °C) or heat stress (HS; 32–34 °C for 8 h/day) environment. On day 28, 12 male birds per treatment/temperature group were euthanized for measuring blood and intestinal health parameters. 0.05% BMD and 0.3% ROD inclusion improved (P ≤ 0.05) the average body weight gain and feed conversion ratio, compared to CON. HS reduced (P ≤ 0.05) average feed intake, bursa and spleen weights, plasma alanine transferase, lipase, and creatinine kinase but increased (P ≤ 0.05) alanine phosphatase and serum immunoglobulins compared to TN birds. HS further reduced (P ≤ 0.05) duodenal villus height (VH):crypt depth (CD), jejunal VH, and VH:CD but this was reversed by ROD and GP, and 0.05% BMD and 2.5% GP increased (P < 0.001) the relative abundance of Blautia and Sellimonas compared to the CON diet. ROD increased (P = 0.010) the relative abundance of Faecalibacterium compared to the BMD diet. The results suggest that 0.3% ROD extract may function as an alternative to antibiotics in improving broiler growth performance and intestinal health.