A new cultivar of hybrid Coreopsis plant named ‘Firewheel’ that is characterized by its compact plant habit reaching an average of 50 cm in height and 70 cm in width, its floriferous and long blooming season of its sterile inflorescences that do not require deadheading; bloom commences in late-June and lasts until frost in Kensington, Conn., its large sized inflorescences with ray florets that are somewhat folded (not flat), ruffled, with serrated tips and are red-orange in color with yellow near the tips, its resistance to powdery mildew and leafspot, its cold hardiness at least to U.S.D.A. Zone 4, and its ease of propagation as cuttings can be taken throughout the growing season.