Well, as I have just put another log on the fire, here are some ideas.
Shut your curtains. We keep the heat out with ours. If you don't have a pelmet (as hot air rises), perhaps a sheet or some towels along the top will help.
If you have an upstairs window facing north, open it a crack to create a draft. Moving air is cooler than warm air.
Three inches of water into a bath with a stool beside it. Don't let the water out until bedtime. Every so often, sit with your feet swishing. When you wash your face with cool water, make sure you wash your ears because you can lose heaps of heat from there. Standing under a shower until you are cool uses heaps of water but sitting in that bath before bed and sloshing yourself over and over will do the same job.
Lots of people recommend a cheap spray bottle of water but that's best in a dryer climate. The water doesn't evaporate properly in higher humidity (I think).
Any clean tea towels or flannels can be wet and put into the fridge. Do it overnight so you have a supply for the day. However, opening your fridge often is highly inefficient so anything you have in the way of a cooler box, ice blocks, frozen water bottles and sorted out in the morning is better. Cover the cooler box with towels to help insulate it.
Set yourself up in a north facing room with your fan or what have you - curtains pulled for most of the day. If you have a more open plan house, set yourself up near the stair case to take advantage of the draughts.
Loose clothing, wide brimmed hat. Long sleeves in the car. If you are wearing a skirt and are in the car, a dry face cloth shoved up your clacker and separating your thighs (drape it over the steering wheel when you get out of the car). Sooo much more comfortable than sweat. A large towel going from car door to car door over the windscreen is a good thing. Try to park facing the sun in that case.
I hope all this helps.