I have this same problem in almost the exact same pattern as yours. It will not happen for awhile, but then bam, it happens one night and then for a few nights afterwards. Also, as you stated, it might just be one isolated night. Also, this isn’t just a bit of sweat; I am literally drenched and have to change clothes and blankets as well.
I get this when I eat a lot later in the night. Sometimes I get so overheated I wake up (all sweaty) but sometimes I sleep through, just wake up wet later.
I’m not seeking a diagnosis, just a discussion of what might be going on. If I can get a better idea of what the causes MIGHT be, I can more effectively lobby my doctor to order up some tests.
I understand. If night sweats are really and truly your only symptom, it’s not likely that testing is called for (although some doctors might do it anyway). If you test when it’s not called for, bad expensive stuff can sometimes happen when little nothing things get blown way out of proportion and more tests and procedures are done to verify or clarify the first tests and procedures. It’s tests and procedures all the way down, like turtles, only with money.
That being said, you might want to read up on hyperthyroidism and/or low testosterone, and see if any of those lists of symptoms ring a bell for you. 
Thanks all for contributing. I hope my fellow sufferers never have another bout.
I get it on occasion and this is one of my triggers I think. When I get cold sleeping I seem to lock in to one position and hold it which makes me cold and gives the sweats. Warming the room up to about 20-21degC makes a big difference, I can kick off the duvet and move about a lot that way.