The room temperature will rise.
A fridge works by drawing warm air in, cooling it, and then putting it back into the main unit.
If the door was open, it will be continually trying to cool the warm air from the room, in which case the thermostat (and motor) will be constantly running (as opposed to running at intervals in a closed fridge).
As the fridge would be running at a much higher rate than normal, it will heat up, causing the average temperature in the room to rise also.
Eventually, the fridge would cause its own death, as it would keep drawing in the heated air it is producing, in a vain attempt to cool it - as the air temperature increases, the fridge needs to work harder to cool it down; the more the fridge works, the hotter the air gets...
I suggest you keep the fridge door closed. If you are anything like me, you would want somewhere to keep your beers cool.