Running a couple of 500GB disks, one 7200.10 and another Hitachi (!) at just under 60 degrees due to the horrible cooling of the NZXT Zero (is = zero cooling for the hard disks). No problems in the drives, both of them are >2 years old. Had a 7200.7 40GB that always ran at 55 degrees, and is still functional, 8 years on. The things that kill disks IME usually are bad controllers (rare), bad connections with the power supply connector, or the power supply itself. Heat, as long as it's under 60 degrees, is not a problem. Heat related failures in hard drives is rare, and usually the actual killer is somewhere else.
I don't think it's the PSU. The TP480 (not the TPII, that was a far worse supply) was one of the better CWT PSUs. It ran hot because Antec had tuned the supply for silence, so there were issues with heavily overclocked setups causing primary capacitor failure, but running at reasonable (<50%) loads would not cause any issues.
The TP480 is a 5 year old model. It was one of my first decent pieces of hardware, bought from Prime in 2003 when I moved to Mumbai. AFAIK that is still doing duty in someone's rig, and it handled everything I threw at it till I needed a SLI setup and later, the 4870X2. It did have two native SATA connectors. On the same cable is no issue, I run three hard disks off a single connector and there's not been any issues.
However, I would heed Bikey's advice and check the voltages. If the 12V line is below about 11.7, you have an issue. Anything above that and you're fine (allowed tolerance is till 11.4, but the TP480 maintains a 3% regulation). A quick look at the BIOS will tell you whatever you need to know. VX450 is a good supply, albeit a little pricey now, but is a terrific alternative for almost any PC save the really hungry ones. Be aware that a few have sporadic issues themselves out of the box, though rare it is not unheard of either.
On the disk failures, it does seem worrisome that a new drive would show up bad sectors, but entirely possible. Just request a replacement. As a practice, I always format a new drive in DOS mode in slow format mode. The bad 'uns usually show up here, so I can start using the drive reassured that it is fine. And this is not a issue of chance, it happens all the time, and not only to Seagate drives. A brand new WD640AAKS drive did the same thing to me, just would not spin up or initialise, new out of the box. WDs fantastic RMA scheme saw to it that I was up and running, with a 750AAKS no less, in 5 days' time. And this was a twin purchase too, bought two disks together. So don't worry, the quality of quality control has gone to the dogs, that's the real answer. And not just for Seagate or WD or computers, life in general has much less QC overall

Where possible, RMA and don't worry about it, and always keep a backup.