How effective would a normal refrigerator be as a replacement for air-conditioning?

Not very, the fridge is designed to cool a small area not a whole room. It also does not circulate air. You’ll likely end up burning out the compressor before you notice any cool air.

Absolutely useless unless you are living inside it.

Totally worthless. The heat that is removed from the inside is released by the coils on the back or bottom of the fridge, so the heat in the house/room stays the same. Actually, more heat is generated by the electric motor that drives the compressor so the ambient air would get warmer and warmer. The cooling coils (condenser coils) must be on the outside of the house, or the heat from them expelled to the outside for the unit to cool the inside of the house properly. And you have to have the proper amount of BTUs of heat removed to make it comfortable. I don’t know what a refrigerator could do, but some small window units are rated at about 5000 BTUs. I have a 2-ton unit on my 720 sq.’ house that does 24,000 BTUs. (A BTU or British Thermal Unit is the amount of heat required to raise one pound of water one degree centigrade at sea level.)

What about if you put a fan inside the fridge to blow the colder air out?
@kritiper the OP did say the heat bit would be outside

@Stinley Depends on the size of the room and the BTU capability of the refrigerator. And you would have to install a fan to blow cooling air across the coils on the outside as well.

Those compressors are not designed to run continuously. This would not work for long. A window ac unit would be much better.

I would think the fridge would burn out rather quickly. It might work for a while, but I don’t think it would last for many months. Just a guess, I really don’t know much about the engineering.

Leave the fridge where it is supposed to be and make an air conditioner out of a high quality styrofoam container or plastic drink holder thing like an a Igloo brand. Cut a whole on the top for a small fan face down. Another hole on the top for a short pipe where air can blow out. Fill the thing with ice, turn on the fan, and the air coming out will be around 40–50 degrees. You can run the fan on solar or batteries if you don’t want to use electricity.

”and the air coming out will be around 40–50 degrees.”
I want to cool the room down, not turn it into a sauna.

Fahrenheit. Around 9 or 10 C.

You can turn the thermostat way down and get that air much colder.

Keep in mind that the evaporator (the inside cold part) isn’t designed to cool air otherwise it would have fins like a regular A/C. Not efficient.