When a window air conditioner is turned off but still plugged in, it does not actively cool the room. However, the length of time that the room will remain cool will depend on various factors, including the insulation of the room, outdoor temperature, and the size and efficiency of the air conditioner.
When you turn off the window air conditioner, the cooled air in the room will gradually mix with the warmer air from outside. The rate at which the room warms up will depend on the temperature difference between the indoors and outdoors, the insulation of the room (such as insulation in the walls and windows), and any heat sources inside the room (such as appliances or sunlight).
If the room is well-insulated and there aren't significant heat sources, it may retain its coolness for some time, ranging from a few minutes to a few hours. However, on a hot day, the cooling effect may diminish more quickly.
To maintain a cooler indoor environment for a longer duration without running the air conditioner, you can implement some strategies such as closing curtains or blinds to block sunlight, using fans to circulate air, and avoiding activities that generate heat (like cooking on the stove). Additionally, improving insulation and sealing any air leaks in the room can help reduce the rate at which the room warms up.
It's worth noting that the specific time the room will stay cool can vary significantly depending on the factors mentioned above. If you need sustained cooling, it's generally more effective to keep the air conditioner running or explore other cooling options like central air conditioning or ductless mini-split systems.