It is normal for the air conditioning system to work more effectively when the engine is warm because the engine provides power to the compressor that runs the air conditioning system.

When the engine is cold, the compressor may run at a lower speed or not at all, which can affect the cooling efficiency of the air conditioning system.

However, if the air conditioning system is not providing cool air even when the engine is warm, it could be a sign of a problem with the compressor or other components of the air conditioning system. It is recommended to have the system checked by a qualified mechanic to diagnose and fix the issue.