I think your question shows a fundamental non-understanding of what warm and cold mean.
In reality, there is no ‘cold’… there is only ‘non-warm’.
If you open the fridge, you do not let out the cold, you let in the warm.
If you switch off the process that cools the air in a room, what exactly should keep the air from warming up due to heat exchange with the walls/ceiling, or being warmed up by the people inside it?
A/C means you spend energy to remove energy in the form of warm air. If you stop this, why exactly should the room NOT warm up?
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