You can check yourself.
Run your computer for a while. Do average work. When you turn it off, immediately open the case and touch the top metal part of the HD.
If you burn your fingers, get a fan. If it is very hot, but bearable get a fan or passive heatsink. If it is mildly warm, leave as is.
The Barracuda IV is one of the warmest new drives, and does not need any extra cooling. Early 7.2 kRPM drives did need cooling though.
One of the servers delivered to us had 2 IBM 10k SCSI drives with no cooling at all - was equipped with cooling immediately.