Mechanicals can do this. A sound transducer needs to vibrate air. The head positioner has a periodic motion, aka vibrations. The head positioner can vibrate the frame of the drive, a flat cover on the drive, the side panels of the mounting cage, etc., which displaces air in a periodic fashion. Hence, the head positioning system is humming along, being told to look for something first here then there then back again. You ear hears a nice beep. High school physics at work.
The refrigerator trick is valid but only as a last resort because the cold temps can reduce bearing life drastically due to contraction. The duration of frozen-ness can be extended with technical freeze sprays (Contact East, for one, carries them). Using the freeze spray, keep blasting the drive until you get the data, but beware that when the drive warms to room temp (this also happens when you run out of freeze spray), it may be covered with frost which melts and...... water water everywhere.
HTH.