Can immunosuppressants cause low body temperature?

No (not directly) If a person become seriously infected (septic) while on an immunospressant they can have a low body temperature. Drugs that directly cause low body temperature include meds for anxiety, depression, alcohol, beta blockers, opiods, and general anesthesia.
Immunosuppressive . Typically that is not a usual side effect. Using Acetaminophen or nsaids can cause a lower body temperature though even that is minimal.