So I'm copying content worth 1TB to my new hdd and it'll take 10 to 12 hours.

Will either HDD be damaged if they continuously transfer data for that long?

Nope.. Unless you decide to move them around while copying...

Should be fine, Hard drives are stress tested being written to for weeks/months before they get cleared for sale.

If it becomes too hot put it in the freezer for a couple of minutes.

Thanks guys, they have been copying for 3 hours now and the external drive is getting warmer.

Shouldn't be a problem at all with modern drives.

Not at all.  It's actually worse for HDD's to allow them to spool down (during sleep mode), than it is to allow them to constantly be running.

I run my PS4 and PC 24/7. HDDs (WD anyway) are built like tanks nowadays.

Don't worry. I've personally moved 3TB of my itunes folder to a backup drive. It took 14 hrs. They are designed to deal with it. I do suggest once you're done to give it a break and cool down.

PS4 might well keep the HDD spinning up but if your PC has more than one drive that you're working from most likely a lot of the time the other drives will not be touched and will have stopped spinning.

Got the majority of the stuff I use all the time on my PC on my primary SSD, then got movies/older games/music split over 3 magnetic drives inside the case which only spin up if I'm using that content, rest of the time tis lovely and quiet in there.