I thinking testing in the night to make sure the sweats aren't caused by hypos - have a chat with the hospital about your symptoms too and what you sugars are. Are you going to bed ok and then waking up high, having woken with sweats in the middle? Do you test when you wake up sweating? I'm sure hypos aren't the only thing that can cause sweating at night hence talking to the Drs, but through testing in the night hopefully you can work out what is happening and whether it is a hypo.
Also you know the dawn phenomenon thing…I always thought that it was a natural rise in blood sugars that some people have pre getting up - so my sugar can be all nice at 6 all night then once I start to move it starts rising - no hypo in sight during the night. If I have had a hypo in the night or day for that matter and if I have dropped particularly low or it's been a persistent low then I do notice a 'liver dump' type thing where my sugar level can zoom up fairly rapidly and not just the little rise that I normally get from have 10g of quick stuff to get me out of a hypo, really high into the teens - so I class that as going hypo in the night with a rebound (liver dump) and not a 'dawn phenomenon' or have I got that wrong and hypos and dawn phenomenon are actually the same thing?