Are you sure its mold and not just soot or dust?
Mold needs moisture. Moisture can come from leaks or from condensation. If you have no leaks, and its not soot or dust, then you have condensation. Condensation is cause when you get warm and cold coming together.
First clean the mold off with bleach solution. Done. Then just dry dehumidification and see if it comes back or not. Air conditioning is also dehumidification FYI.
Oh, and you can get a moisture meter to check for moisture. Cheap ones are not too accurate but probably sufficient for your purpose.
Here is a good enough one for $20