With AIDS, the whole immune system is not non-functional. The condition results in a severe drop in CD4+ T-cells, which is what primarily predisposes AIDS patients to secondary infections.
Fever can be an immune response to infection, but it is not directly affected by the loss of CD4+ T-cells. Rather, fever occurs due to a complex cascade of events triggered by pyrogens, which causes a release of prostaglandin E2 (PGE2). In the hypothalamus, PGE2 signals a systemic response for the body to generate heat. More on the pathophysiology of fever can be read here.
AIDS patients still produce PGE2 in response to pyrogens (such as compounds produced by bacteria). Therefore, AIDS patients can certainly get fevers. In fact, AIDS patients may be more likely to get fevers because they may produce more PGE2.