Latey, probably more information that you wanted to know....
The laptop runs hotter when plugged in mainly because of power management. When the machine is on batteries, it throttles the processor's speed (clock frequency) to extend battery life but when plugged into the mains, the settings via Windows or a manufacturer helper app and driver or BIOS allow the processor to run at full steam. Charging the battery does add more heat, but most of that will be made in the adapter, not the machine itself.
Processors have an on-chip temp sensor and will shut themselves down if it starts getting into the overheat zone. Many machines have a temp monitoring capability in the BIOS screen and there are some free programs you can download that will tell you how hot your processor is running and even the fan speed.
While it could be related to the hard drive replacement, and a compatibility check might be in order, you might have an overheating processor. The noise could be related to the fan which all recent build laptops would have unless they are Macs which you do not have.
The whistling could be the fan motor, the hard drive motor, or an electrical short causing an internal switching power supply to run amok. That last one would not be good. Look around for vents and when you have used the laptop for a period of time you should be able to feel a warm light breeze coming from within at one of the vents. That air coming from the processor fan.
Good Luck!