Interesting question…quite a few diseases cause a rise in your body temperature and can cause excessive sweating often this is caused by your body trying to fight off the disease.
Of course sweating causes you to lose moisture and so it can cause dehydration this is part of the reason why you often hear people instructing sick people to drink plenty of water and is also why people in hospitals are often put on saline drips (these drips are used to deliver drugs but also just to replace water a patient has lost while sick). Any disease that causes fever can potentially lead to dehydration, however I know of no disease where sweating on its own can cause death (unless the sick person is unable to replace the lost fluid through drinking or eating).
Many diseases do however kill through dehydration, perhaps the most famous is cholera caused by a bacteria called Vibrio cholera. Cholera causes serious diarrhoea and vomiting still kills around 100,000 people a year, which is particularly bad when you realise that with modern treatments it should be less than 1% fatal. However the diarrhoea and vomiting that cholera causes are so bad and drain a person of fluid so quickly that it is often difficult for doctors to get enough fluid into the patient.
Although cholera does not kill through excessive sweating it does kill through dehydration and shows that any disease that causes you to lose body fluids is potentially deadly. In general though diarrhea and vomiting will cause a person to lose more water than sweating so they are more likely to cause death through fluid loss. As I said though if a person is not replacing fluids then they will dehydrate through sweating.
So don’t forget to listen to your doctor and drink plenty of water when sick 🙂