Choloepus didactylus has reduced metabolism and difficulty in thermoregulation owing to its low body mass, and there are few studies related to the vascularization of abdominal and thoracic organs in this species. Therefore, we macroscopically described the arteries that comprise the aortic arch, thoracic aorta, and abdominal aorta. Six specimens were used, and their arterial systems filled with red latex before fixation in 10% formaldehyde, and fragments of the rete mirabile were processed for histological analysis using light and scanning electron microscopy. In these species, the aortic arch had two branches: the brachiocephalic trunk and left subclavian artery. The initial portion of the abdominal aorta presented four different ramifications, besides to the peculiarities of the adrenal, renal, and iliac arteries. Microscopy of the rete mirabile revealed a muscular artery surrounded by smaller muscular arteries, veins, nerves, and lymphatic tissue joined by connective tissue. Thus, the data obtained have clinical and surgical importance, with applicability in procedures involving vascularization of the thoracic and abdominal organs. We suggest that the rete mirabile is an efficient thermoregulatory structure because it allows the accumulation of blood and the countercurrent heat exchange, as there is no blood mixing.