arugula in 100 weather? please. Plant okra, malabar spinach, and/or amaranth. Possibly sweet potatoes.

What do you mean by 2-3 hours partial shade? Do you mean it gets full sun the rest of the day outside those 2-3 hours?
I second Glib's suggestions, and I don't think any of the veggies on your list would work. Watermelon may also work if you provide sufficient water.

I'm assuming you're asking about fall, after the 100F temperatures cease. Now, around here, that's pretty much October. I find sweet peas do marvelously over the winter. Plant in November, and harvest in March. They'll endure temps down to the low 20s, but do fine as low as freezing. 2-3 hours of shade is no problem for them.

Not sure about squash. I consider that very much a summer veggie.

If you planted peppers now, they'd do fine until it got pretty cold. They are, however, completely intolerant of frost.

You could also do an early fall crop of tomatoes, though it might be a challenge to find them in your local stores then. They too are frost intolerant.

Does 2-3 hours of partial shade mean full sun the rest of the time? If so, the only thing on that list that might do well in the summer is squash. If it is only 2-3 hours of partial shade, the plants in that area will probably be happy with the break in the intensity of the sun. I agree with glib, although you could probably also at least try beans, tomatoes, peppers, cukes, etc, if they are getting a break from the sun.

Everything else on that list would likely do better in the fall/winter.

i read the OP as saying she gets 2-3 hours of sun a day - i don't know why now looking at it - partial shade is unclear - but based on what her other suggestions have been so far, and based on the title of the post, and the "large shady tree". perhaps she meant 2 - 3 hours "dappled sun"?

brooke - can you clarify before we totally confuse you with conflicting lists?

from the OP: "any ideas for vegetables that will tolerate the heat and the shade?"

I think this is why other folks have suggested winter veggies like spinach etc....but some/most of those plants will have a hard time in those temperatures.

Lettuce would be a good thing to start with as an experiment - I like the mesclun mixes from botanical interests - sprouts quick, inexpensive, quick results. Why not try it and see?

Here is a link that might be useful: Sassy Salad mix

Also, let's be clear that you're NOT talking about 100F crops. Your talking about fall crops (as in, NOT summer crops) after the 100Fs are over. That's right?

Yes - that's important to clarify.

Are you in SoCal by any chance? Sounds like our climate with the hot autumn weather....if so, you should be able to grow some things this summer in partial shade - before it gets so hot.

Thank you for your replies! I only get 2-3 hours of partial dappled sun total a day because of the large tree. I'm looking to plant in the fall due to the extreme heat of the summer. I'm in Arizona.

I would like to have a good idea of what to plant in the fall/ spring seasons so I can start researching more specifically about the vegetables you all suggest. This past winter it didn't get below the high 30's ever. The suggestions I was given originally were from the Arizona forum.

To be clear the rest of the day the patio is in complete shade

Thanks for the clarification. In that case the list from the Arizona forum does sound like a very good start. I would add, potentially:

carrots
turnips
chard
herbs, maybe

Thank you I will add those to the list! I'm using a planting calendar from the state of Arizona for when I'll plant the different vegetables

I have an area just like this. I have it planted in flowers but I also plant chard, kale and cherry tomatoes, plus a native chiltepan pepper.
We use the chiltepan peppers dry and crushed in a pepper grinder in place of pizza red pepper flakes.
My chard seeded itself this year from last spring.
In this area is also some Parsley, basil and hyacinth beans, plus some bulking flowers and tropicals.
I've had huge crops of Armenian cucumbers and squash in this area, too.
Also, during cooler seasons I plant salad veggies like lettuce, spinach and radishes in my shadier spots. Cowpeas will do okay but better in sun.