A few incoherent thoughts,
- Bear in mind a fan will actually heat up the room you are in: It makes you more comfortable due to the air movement over you, but there is still an electrical appliance on in the room, and some heat will be generated here.
- Shades are also a good idea to make you more comfortable, but if they are on the inside of the window, the air temperature of the room is still increasing as the solar gain has already made it in to the room.
- External blinds would stop the direct solar gain, as would anything else. stupid idea, but why not tape some kitchen foil up on the outside face of the window!?
Daylight, be damned, but it will slow down the solar gain.
- Do you know if the 'central air system' is actually working? Also if the outside air is too hot and there is no cooling applied to this central air system, this air will not necessarily cool the inside air down.: File a complaint with the landlord and tell him the fan isn't working, or isn't working to duty. He might at least go and have a look at it, whether you are right or wrong.
- Also sounds to me like there is a bit of an issue with ventilation generally, high external temperatures notwithstanding. In the UK I could not get away with designing an occupied space without at least some reasonable natural ventilation or up to 4 air changes an hour mechanical ventilation. Remember also someone will have to paint that room at some point, without reasonable ventilation the painters and decorators are liable to end up 'high'.
- Remove / Reduce internal gains, switch off unneccesary lights / appliances / fridges etc.
- Make yourself more comfortable by increasing airflow over yourself, and getting out of the way of the sun. Also take off your clothes.