Now it's time to check out your apartment's heating and air conditioning unit, also called an HVAC unit.
Make sure that the thermostat works and gives an accurate representation of the temperature in the apartment. Also, the unit should be able to blow both hot and cold air. Check to make sure that is does. Check to see if there are any loose wires or hoses sticking out of the unit itself. It should not be leaking water either.
Also, make sure the filters have been replaced recently and are not clogged or dirty. The previous tenants may not have put them in at all, so it's going to be your job to put new ones in. Change them out every few months -- if they're dirty, they can cause the HVAC to run inefficiently and drive up your energy bill.