My $0.02 worth..
If it is an electric baseboard I would worry. If hot water (which I doubt) it's probably not a problem.
Reasons for my thoughts: A hot water system can only get so hot - even if for some reason it boils the temp would still be way below the flash point of most normal materials they make curtains out of. (Don't think there are any brands making curtains out of gun-cotton..)
Electric on the other hand could, even though highly improbable, develop a short which can rapidly exceed the flash point of just about anything. I've seen way too many things that I thought impossible happen with things electric thus I've learned that paranoia is the best approach..
;-)
I think I contracted your paranoia before I finished the comment! So I used duct tape to “shorten” the curtains, so I’m good, thanks! ;o]