Since I recently acquired a BDP-3, I was able to answer my questions.
I installed a Western Digital Black 750 GB hard disk drive in my BDP-3

There were no issues with heat. After the player sat idle for 13 hours, the following measurements were taken
with a Fluke model 561 infrared thermometer:
Processor heat sink: 125.8 degrees F
Transformer coil: 106.0 degrees F
Chassis bottom: 101.3 degrees F
Hard disk drive: 98.0 degrees F
Note: The BDP-2 and BDP-3 do not spin down drives after a period of inactivity. Be aware that if you install an internal hard disk drive, with no power conservation feature, such as the WD Black drives, it is going to spin 24/7. The external hard drive enclosure that I use (Rosewill Armer 304X-APU3-35B) spins down the drive after 20 minutes of inactivity.
After playing music for 3.5 hours, the following measurements were taken:
Processor heat sink: 129.2 degrees F
Transformer coil: 106.2 degrees F
Chassis bottom: 102.7 degrees F
Hard disk drive: 96.6.0 degrees F
Music from the internal hard drive sounded better than music from an external hard drive with its stock power supply and stock USB 3 cable.
When I upgraded the external hard drive's power supply, music from it sounded better than from the internal hard drive.
When I upgraded the external hard drive's USB 3 cable, music sound quality further improved.