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The presence of chills ad rigors at night, in a diabetic patient, could be a sign of infection within the body. The most common causes of such asymptomatic infections can seen in the urinary tract, bones, or the skin.
Hence , it would be best if your grand mother consults her doctor for a comprehensive examination and tests including a complete hemogram, blood cultures, urinalysis, urine culture and sensitivity.
Treatment can be with prescription antibiotics, provided by your doctor.