Folks might be better able to help you diagnose the issue if you gave them all the details...
Under normal circumstances, the condenser fan will only run (be powered) when the a/c compressor is running, however, if the a/c control system senses an engine over temp condition it will disable the compressor and run the condenser fan, even if the a/c system is turned off - if your condenser fan is running as soon as the ignition is switched on, the system is most likely sensing an over temp, even if the engine is off and cold.
Air condition systems require specialist tools & experience that many people do not have - if you lack these, take the car to an a/c specialist and have them diagnose the problem - the diagnoses involves analysis of system pressures which can be affected by local climatic conditions and is not something that can be done via internet forums.