The whine and the temp variations could be related; the thermo could be bad, and the clutch could be tightening and loosening randomly (maybe a result of the thermo going bonkers).

Although thermostats usually fail in the closed position, I have seen aftermarket thermostats flex and bend the pellet support, causing the thermostat to partially fail in the open position. The better ones (cost a couple $ more) have this area beefed up to eliminate the problem.
If yours is indeed stuck open, and the fan clutch locks/unlocks randomly, that could be the whine you hear and cause the wide swings in temp.

Contrary to some posts, what I have observed of a good fan clutch is that it will turn very free under normal engine temp conditions, under 100 degrees C. You can raise the hood on a just-driven car, and spin the fan 10 revolutions with one hard flip of your hand. If the AC is on and has the electric fans running, the clutch fan will spin freely like that.
When the motor is stone-cold, or quite hot (over 100C) without the AC electric fans on, the clutch tightens up and will spin only one turn or two by hand.
That's just a rough way to check general condition of the clutch.
I only hear my fan roar for a few seconds when I sit in traffic with the AC off (no electric fans on) and get things good and hot - water temp over 100 -then accelerate up to speed.

DG