In the current heatwave conditions in Australia, it is important to remember that it isn't just any day, but a special situation. Your needs and your baby's needs are paramount.
How to keep cool
If you have air-conditioning, even in one room, this is a great help in keeping your baby cool, and yourself, too. Without air-conditioning, hanging wet towels on the backs of chairs and directing an electric fan at them, can make the air that circulates a little cooler. (Evaporation cools.)
It can be important to sponge your baby with cool water if she becomes hot or red. You may need to do this several times a day. On scorching days, the water in the "cold" tap may actually be hot in some regions. If this is so, pour some water into a bowl and put it aside for a short time till it is cool and safe to use.
You will realise that this is not the time for dressing your baby in onesies and jackets. Indoors, just a nappy is often enough in a heatwave. If you absolutely have to go out and cannot avoid it, loose cotton clothing is best, with a cotton wrap to keep the sun off delicate skin, e.g. when you take your baby from the house to the car.
Of course, going out may be a Good Thing if you don't have air-conditioning. Lots of mothers and pregnant Mums spend a few hours at an air-conditioned shopping centre or a cinema. Does your local library have quiet activities for very young children?
Beaches are NOT safe places for babies in hot weather. Besides direct sunlight, there is reflected light (and heat) from the sand and sea, and the windscreens of cars in the parking lot. The same applies to pools that aren't fully shaded. So check out how good the shade is, first.
Infant-care lambskins are useful as a surface for a baby to lie on as they absorb about one-third of their weight in water before they feel wet. I was lucky enough to be one of the mothers with a new baby in a trial of infant-care lambskins, while living in a remote arid region, and it was a good experience. (No, I have no conflict of interest in mentioning this as I had no financial benefit from the long-ago study.)
For yourself, loose clothing is your coolest option. This isn't the time to catch up with heavy housework - just the basics. Forget what you "should" do - it's more important to focus on keeping you and your baby cool. This can be a time to watch a DVD. You may find you are not hungry in the middle of the day, and a cool soup or a sandwich or small salad might be all you feel like eating. Then in the evening your appetite is up again. Like so many Mums now, you probably carry a water bottle so that you can take a swig any time you need to. Your urine is a good guide to whether you are probably hydrated; if it becomes dark, that means you need to drink more fluid straight away.
A breastfed baby needs to have unrestricted access to the breast, which will supply all fluid needs, changing through the day in response to your baby's demands. You may find that your little one takes quick "snacks" at the breast in the heat of the day, spending longer at the breast and having big feeds after the sun goes down and in the early morning. A study of breastfed infants in the hot, extremely arid Negev desert found that they remained adequately hydrated if they had unlimited access to the breast. (This may not apply to formula-fed babies, who may need small amounts of additional water on the hottest day - but check with a Child Health nurse in your area.)
A darkened room is cooler. Drawing the blinds or curtains keeps out the heat, whereas opening them, or having sheer or lace curtains, lets in the heat with the light. With thin curtains, or with the curtains opened wide, often even the wall opposite the windows feels hot to the touch.