Which type of immune deficiencies in infants would cause low grade temps?

Immune deficiency? Many immune problems can cause low grade fever, but autoimmune disease has usually specific findings other than fever. Low grade fever in children may be normal. Children will frequently have higher temperatures for any illness than adults. You did not say how the temps were taken of when. This info is needed for a good answer! but if a fever is present, i would bet on low grade infection!