I live in Arizona. I have a 2 year old avocado tree in a pot, not in the ground. Last week it was exposed to the extreme heat wave that hit us. I made sure the soil was moist every day. Twice a week I use the pond's backwash to water it. This week the leaves are brown and drooping. Can I save it? Should I bring it inside? I have it under a shade umbrella but it still gets sun in the afternoon. Is it too late?
I'm guessing you live in a hot part of Arizona (because you're growing an Avocado tree). So, this link provides some helpful information on growing Avacado trees in the desert. Basically, the author says to use the right variety (the author recommends Aravaipa), the right location (eastern sun and evening shade) and the right soil (the kind the author is recommending isn't entirely clear to me from the article, but I have some insights).
Anyway, some soils (like our amended clay-type soil) are cooler than others. So, that may help to keep the roots cooler in the heat.
Growing it in a container is going to be more problematic in the heat, since it'll dry out faster, and because the soil will get hotter. If you could spray some paint or something on it that reflects infrared rays, that would probably help to keep the container cooler. Or if they had a kind of plastic coated with something that reflects it, that may work for ground cover to prevent the ground from heating up.
There are other tricks to help plants with heat and aridity tolerance (like making sure the pH is right for your tree, adding extra organic matter, making sure the nutrient profile is right for extra-high temperatures since some nutrients aren't as available in the heat and some are more available, showering your tree with water regularly, planting it where it won't get wind from many directions, etc.) However, unless you have a variety suited to the desert (as well as other conditions to help), I would probably just bring the tree inside to save it, unless I wanted to risk it dying. You could try, but I would consider it an experiment.
If you do plant it in the ground, be very careful of the pH. It's likely that you have a soil with a high pH, which may be particularly challenging (and may be the reason why you're using a container).
I can't tell the state of your plant without a picture but I don't see any harm in bringing it inside with the heat you are experiencing. You ca take it out for a few hours a day if you can do that but leave it inside during the warmer parts of the day. In addition to that, the type of pot will matter. If you are using a clay pot, it can let water out more easily than say a plastic or glazed pot. So, you may want to consider changing pots at some point if that is an issue.