Do refrigerators struggle with too warm a temperature setting?
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
--------------------------------------------------------
    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)
-----------------------------------------------------------------------
    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.