Foam board insulation over drywall
If the apartment is a 8" thick "cinder-block" wall with no insulation, then it's R value is likely around 1.5-2. If it's a concrete wall, it's R-value is around 3.8-4. 

In any case, 1" thick polystyrene foam has an R-value of 5, and ½" drywall is about .5, so adding the foam and drywall (combined R-value of 5.5) over your existing drywall will more than double the wall's insulation value (in the case of concrete) and almost quadruple it (in the case of cinder block). All assuming there really is no existing insulation. 

I would say the wall will become dramatically cooler.