Sometimes it helps to be my age and have memories of how we beat the heat in those "no air conditioning" years!
Close all windows and draw all drapery first thing in A.M. to hold any coolness night may bring.
Strange as it seems, drink hot beverages to cool off. (When you visit Houston you'll find this is common.)
Take lukewarm showers, not cool.
In baths put some baking soda to beat heat rash.Also useful when washing and dusting baby.
If you can get blocks of ice, (bags of ice cubes work too) place in a washtub, have a fan blow across the ice to cool one room.
A flannel bottom sheet will actually be cooler than a slick one.
Wear cotton - best cooling fabric is seersucker, next Palm Beach cloth for men's suiting.
Eat small meals more often rather than big meals.
For animals - usually a dog will find a spot under a tree or behind shrubs, find that spot then dig a hole several feet deep, drop in several bags of ice, (puncture to allow melt to run off) refill hole. The ice will keep the spot cool and help dog cope. Provide lots of cool water. If animal gets wet, lie you hoase the dog down, be sure to dry thoroughly using cool setting on hair dryer, especially under "arms." Else a mould develops which is murderous to clear up. (A hot setting on a dryer can raise an animal's blood pressure and cause death!) Keep cats indoors and dogs away from beaches. The sand works into fur and causes all kinds of irritation, hot spots etc. (Cheaper to take the time than pay those Vet bills!)
Last and by far not the least : Tape a reflective material onto the top half of windows to reflect sun away. shiny side outward. Silver foil - the kind used for cooking and freezer storage - works like a charm. Will usually drop temp in house about 15 or 20 degrees.