laptop -> dont know, but mine also very hot (~60-70) but been working for 6 years with extreme abuse and no important data so i dont care.
pc -> improve airflow. or apply thermal paste and stick some heatsink fins to it lol.
A different power supply isn't going to make a difference.
If it's an internal drive, use a program that reports SMART data (such as DiskCheckup) to show the temperature being reported by the drive. 45 to 55 Celsius seems to be a very safe range of temperatures for a hard drive - if the drive is consistently above 60 C then you probably need to improve the drive's cooling. Make sure that a stream of air is moving freely over the top and bottom drive surfaces to carry away the heat.
What are your system specs ? -- could be that you are low on system memory so the HDD is always running trying to keep the swap file updated to keep the system running if you are out of systeem RAM available.
It's a destop pc with just the one internal hard disk which is resting on a tray that allows air flow from all sides. It doesn't support SMART data and I don't have a suitable thermometer to test the temperature but if the computer has been on for 8 hours or so it gets rather hot. The temperature in the actual case is cool (I know that's quite meaningless).
Unless anyone has another suggestion I intend to leave the hard disk in there for a while just to test things. At least I won't start experimenting with different power supplies...
There isn't a fan that is targeted at the hard disk but there's a general flow of air from the front of the PC and out the back. I've just taken the side of the PC off to get a little more air in and it does seem to have cooled the hard disk so perhaps that's it, it just hasn't had sufficient cooling.
If there's too much space around the drive then the air won't be forced to flow directly over the drive surfaces and temperatures may go up. So taking the side off the case probably won't help, and it may actually hurt.
You want to make sure that the fan is exhausting a decent volume of air through the rear of the case and that most of the air intake is forced to flow over the drive and isn't coming in through some other opening.