Congratulations, you've just stumbled upon the secret self-destruct feature that all manufacturers design into their appliances... NOT! (^-^)
There is no setting of a refrigerator's controls that will "overload" a refrigerator (barring extremely abnormal operating conditions). It would certainly not flicker like that.
Believe it or not, manufacturers don't like to have customer complaints and returns, it's bad for business. If there was such a defect, lawyers would be all over it, too.
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With one exception, the warmer the fridge/freezer is set, the less it works and it will not overload.
Not counting the energy lost to opening the door, or to the initial cooling of warm things, the energy a refrigerator requires is roughly:
(RoomTemp - FridgeTemp) * The compartment's surface area
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The average R-value of the fridge's insulation
The R-value and the surface area are fixed by the unit's design (with one exception). So it should be obvious that raising the FridgeTemp lowers the required energy.
For example, suppose your refrigerator compartment is 26 by 27 by 38 (inches) and the average R-value is R-19 (US, not SI). Assume a constant, summer-time room-temp of 76°F.
Then, a fridge set to 34°F would use roughly:
(76°F - 34°F) × (2×26×27 + 2×26×38 + 2×27×38)(inches²)(ft²/144 inches²)
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19 (ft²×°F×hour/Btu)
= about 83 BTU/hour or about 24 watts.
Set the fridge to 40°F and it drops down to 71 Btu/hour (21 watts).
See R-value (insulation) for more information.
The exceptions:
If a freezer is a frost-free model, it uses extra energy to stay frost free. On many models this just runs off a timer, so the temperature-setting has little effect on how much energy is used. On smarter models, the energy use increases with the room's humidity and how often the door is opened plus how full the box is (fuller is better).
If a freezer is not a frost-free model, and ice builds up. This decreases the effective surface area and increases the effective R-value. So, the unit uses less energy, but items in the box usually remain too warm, too long -- leading to greatly increased spoilage, poor ice making, etc.
So turns out the water valve in the back of my fridge was bad. All rusted out. I broke down and called a technician (thankfully) and he said we were lucky it didn't burst, as it probably would have flooded the house. On top of that, the condenser fan motor was dead.
I suspect the former owner knew all of this, and just had his guy go behind the fridge and shut off the main water line to the fridge so they wouldn't have to deal with it before selling the house.
Best Answer
Commercial refrigeration units are available which place the compressor in a remote location. There's a good summary of the pros and cons of such a setup at Katom Restaurant Supply which is rather comprehensive.
One thing to consider is that a typical home air conditioner is about the equivalent of a refrigerator with a remote compressor.
A post two years ago on Houzz website has about 20 comments with nothing conclusive with respect to residential systems, but the expected reference of commercial/restaurant sources.
I'd expect that you'd have to pay the premium for a commercial unit.