Excessive perspiring was one the first symptoms I experienced in the weeks leading up to my diabetes diagnosis, and is my first clue that my blood glucose is too high. How's the thirst levels?
If you're perspiring to excess without significant exertion, or when you eat, I'd be more inclined to do a spot blood glucose test (if himself hasn't got a glucometer, I'll bring a spare lancet next time I come up) and see what it is like. If it is out of whack, I would suggest a fasting BGL test, and possibly a trip to your gp. I mean, you're pretty young to be thinking perimenopause (I'm not saying it doesn't happen, I'm just saying it's unlikely in your thirties except through premature ovarian failure for any one of a multitude of reasons, or of course, surgical menopause). I'd also be tempted to think there might be an issue with your thyroid levels - I'm thinking it's time you had a chat with your gp anyway and had a complete hormonal assay (and perhaps a fasting BGL) done (it's the only way to know for sure if you're in perimenopause anyway) - it will help set your mind at ease :)
(Oh, and my personal experience with years of hot flushes - it starts creeping from the inside, and feels like someone lit the furnace and turned it up to 'surface-of-the-sun' level. It's pure heat. It's not just perspiration. It's not just feeling a bit hot. It's not just a warm atmosphere. It literally feels like there's a sun going supernova inside you and it's trying to get out or melt you from the inside trying. And mum has described her experiences as pretty similar.)