You may not be able to compel your landlord to do anything quickly and the weather may turn before he does anything, anyway, so in the meantime:

Close your blinds (and curtains if you have them) if you're not home during the day so the place won't be hot when you get home. Keep the blinds closed on any sun-facing window if you're home, and open the shadiest window for some breeze.

If you have big enough windows for a box fan, get two and put one blowing outward in a sunny window, and another blowing inward from a shady window, preferably in another room. Reverse the fan direction when the sun shifts. You always want the intake from the shady side, and the output on the sunny side.

It really does help. I lived without a/c for years.