You mentioned Furret purring, but fun fact about actual ferrets and the noises they make. When they're excited and having fun they make a noise that sounds like "dook dook dook". They'll be playing around and dooking up a storm.
Ferrets also do this adorable chuckle when they're having fun (that one's a lot harder to spell in any way that conveys it well).
So I imagine a Furret that's getting excited and worked up dooking and chuckling adorably during foreplay!
Also irl you're not allowed to own a ferret that hasn't been spayed/neutered because the hormones from going into heat can literally kill them if they aren't able to mate. Because of this ferrets are one of the only animals that some people will both performing a vasectomy on rather than neutering, as breeders may need to mate a female ferret for her health, but the pregnancy would also be dangerous at the moment for some reason.
All that to say I don't think Furret will die if it doesn't mate, but I imagine them getting EXTREMELY desperate and needy when they go into heat.
I actually know way more about ferrets than I do snakes, and mustelids (the family that ferrets, badgers, otters, and the kids are a part of) are my favorite kind of animals!
Ooooh, I admit I put in purring because I didn't know what sounds ferrets make, hah. That does sound adorable, though, dooking and chuckling and getting all excited...
And wow, yeah. That's...wild, tbh. I knew vaguely that ferrets can die from heat, didn't know about the vasectomy thing, that's really cool. And lmao, yeah - I imagine Furret would be one of those Pokemon absolutely up there in neediness when heat comes about.
And that's super cool, mustelids are so much fun to think about :)