Need info on air conditioning?

This is untrue. Houses heat up in the winter and sometimes you need to run the cooling mode. If they needed to get the AC to turn on to check it, they could simply lower the thermostat so that it is not satisfied by the indoor temp. Outside temperature has zero impact on the ability to diagnose a potential problem nor does it affect the systems performance in either heating or cooling modes. Odds are they do not have a maintenance guy qualified to look into the problem(as in the case with many apartment complexes) and they don't want to hire outside help. The service call alone should run them at least $100 and a repair or replacement will cost several hundred to a couple thousand dollars. I would keep pushing the issue with them.