Are you saying the system is into thermal overload?
Nope, All conventional refrigerators manufactured today, from the less expensive mini-refrigerator to the high end models, all use one basic refrigeration system that consists of a compressor, condenser, capillary tube and evaporator. The compressor is a pump, because the pump in a refrigeration system is always used to compress the refrigerant, it’s referred to as a compressor. When the refrigerator is turned on, it starts the compressor. Since the intake of the compressor is connected to the evaporator, it begins to pump out some of the refrigerant gas from the evaporator. As the refrigerant gas is removed the pressure in the evaporator begins to drop. If there is any refrigerant liquid in the evaporator it will immediately start to boil because of the lowered pressure, absorbing heat of vaporization in the process causing the evaporator to get cold. The cold evaporator will, in turn, absorb heat from warmer food in the refrigerator. The refrigerant pumped out of the evaporator is forced into the condenser tubing where it is compressed into a high pressure gas because of the restriction presented by the capillary tube prevents it from flowing through as rapidly as the pump can pump it out of the evaporator. As the compressor runs more and more, refrigerant is pumped into the condenser so that it becomes highly compressed and its pressure builds up.
Compressing a gas concentrates its heat and raises its temperature. The hot refrigerant gas, at this point, contains the heat it started out with plus the heat it absorbed from the food compartment.
The highly compressed gas can be quite hot. As the hot gas flows through the condenser coils it begins to cool, giving up some of its heat to the surrounding air. At this point the refrigerant contains less heat than when it entered the compressor even though its actual temperature is very much higher. At this lower temperature some of the gas condenses to a liquid and gives off the heat of vaporization which it absorbed when it boiled in the evaporator. By the time the refrigerant has traveled through the condenser all of it has become liquid and given off all the heat of vaporization it absorbed from the food compartment. After condensation, the liquid refrigerant continues to flow, first through the filter/drier where any contaminants like moisture are removed, through the capillary tubing into the evaporator where it boils again. This cycle continues as long as the compressor is running. In order for the refrigeration system to work properly, some restriction to the flow of refrigerant is placed at the entrance to the evaporator. This prevents the refrigerant from flowing too fast into the evaporator so it maintains a low pressure in the evaporator as the compressor pumps it out at the other end. At the same time the restriction causes the refrigerant to pile up in the condenser and capillary tube raising its temperature and pressure and permitting it to give off its heat of vaporization. The refrigerant from the outlet of the capillary to the inlet valve of the compressor is at low pressure. This is referred to as the low side. The refrigerant from the output of the compressor through the condenser and capillary tubing is at high pressure and called the high side. The capillary tubing offers the restriction necessary to separate the high side from the low side outside the compressor.
Is it reasonable to expect two different new main boards could be defective?
In the appliance world it's not uncommon to get a part that is bad right out of the box. It's rare to get 2 or 3 in a row that's bad but it does happen. Since yours has been replaced three times, at this point I doubt the board is the problem. I'm going to need some clarification without exaggeration:
...the cabinet will go from 30's to 70's quickly.
The cabinet or box is the metal sides, top and back and compartment divider. There's 2" of foam insulation between the box and the compartment liners. That means the coldest the box will get is room temperature or slightly cooler than room temperature. If the box was 30°F you wouldn't need any AC and your hand would stick to the sides.
....will run for 24-36 hrs, then cabinet heats up to 60 degrees for 24+ hrs
The defrost cycle is about 20 minutes long and we've already established the heater will turn off either by itself at the end of the defrost cycle or by the defrost thermostat opening so we can rule out the defrost system completely. When the box heats up you're assuming it's in a defrost cycle and that may not be the case.
My best guess at this point is the condensor fan motor stops working intermittently. Here's what you need to do; Pull the machine away from the wall. When the box starts to get warmer remove the cover over the machine compartment and tell me what's working and what's not working between the compressor, condensor fan motor and the evaporator fan motor (in the freezer compartment).
