Melbourne

I lived without cooling for a long time. You can have icypoles or freeze a little water in the bottom of your water bottle so it stays cold.

Also you can wring out a T-shirt or a bandana in cool water and put it on. The water will pull heat out of you. When it gets warm rewring it with cool water.

Watch your environment too - if there are any windows that face the sun that will heat up that room and probably the rest of the house. Closing the blinds helps but putting cheap blackout curtains over that is another barrier to keep the house cooler. Taping foil over the windows looks bad but that really helps a lot.

Also if it gets cooler overnight let the cool air flow through by opening two opposite windows/doors in whatever way is safest. Then once cool seal up the house before morning and keep the hot sun/outside air out.