Cooling outside of the fire compartment will probably do very little to suppress the fire

This is a video clip from training in an acquired structure.

At the start of the video we can see two cameras on the left side, positioned with the firefighters in the second compartment next to the fire compartment. The normal camera in the bottom shows that the visibility is very bad but the top thermal camera gives good orientation and ability to assess smoke conditions.
On the right side there are two cameras positioned against the entry to the second compartment, behind the firefighters.

At 3 seconds the door is opened to the fire compartment and the nozzle operator starts to cool the smoke and heat coming out with a straight stream in the ceiling. The stream hits a surface in the ceiling and breaks up into droplets which cool the smoke on their way out to the sides and down. The stream also creates a cold surface in the ceiling that prevents offgasing as long as it is cold, and further cools the smoke passing under it.

At 9 seconds the nozzle operator has achieved good smoke cooling in the entire second compartment. The smoke flowing above the firefighters heads against the entry point behind them is cooler and safer.
If the objective in this training was to make that space safe, the door to the fire compartment should be closed as soon as possible. And the firefighter could also spray water over all the ceiling and wall surfaces to make sure they are cold and wet to increase that safety.

At 13 seconds the firefighters stops to apply water. But the smoke continuous to flow from the fire compartment and it reheats the space above and behind the firefighters.

At 23 seconds, 10 seconds after the application of water stops, the second compartment is again too hot and potentially dangerous.

In this example the firefighter only cooled the smoke outside of the fire compartment, to make that space temporarily safe for the firefighters to be in. But the fire compartment is probably not affected by this action unless water is actually directed in through the opening. The flow of smoke moves away from the fire and it also brings all cooling capacity with it, away the fire compartment.

Unless we can actually pinpoint water in through the opening to a fire compartment we should assume that it will not start to suppress the fire in any permanent way. All cooling outside of the fire compartment is thus probably very temporary and requires a rapid reapplication with bursts of water, or a continuous flow, to maintain the smoke cold and safer.