Well --
Being that i've been living thru 95 F temps with a relative humidity of 95+%
Here is my advice --
1) Curtains -- work well to block out heat from sunlight. I would not Wet them -- that will just add more humidity to the air and make it uncomfortable. (assume you aren't a desert climate) -- a better option is UV reflective Tape for the windows (Like the same stuff they use to Tint Car Windows.)
2) Look at using a dehumidifier in the flat.
Lowering the humidity in an area makes high temps at least bearable. -- problem, with a de-humidifier unit is that they tend to produce warm air as part of the process.
Combine this with a couple of good size box fans pushing the air thoughout the flat, and you might find it more bearable.
3) Look at getting an A/C unit -- you get the general benefits of dehumidifier, cool air and a breeze from it.
just my thoughts
dB