@Maryl
I'm in Zone 7a in north central Texas about 50 miles east of Abilene, so I'm guessing the parameters you have outlined are something I'm familiar with. The heat and sun all day are no joke and sometimes and some years plants have trouble coping. I'm going to list and illustrate with some photos of some that manage the conditions pretty well.
First one I thought of was the Paper Spine cactus that Thijs suggested. I took it out of the sun this year and relocated it to hanging under an oak tree where it still gets blasted by the sun and endures a lot of heat, but not quite as much. The reason for the move was how easy the growth detaches from the plant. Last year something was removing and carrying off all the new growth. So far the move has kept that from reoccurring. I don't know the nature of the thief - bird, squirrel, rat, possum or what. Here's a photo of Tephrocactus articulatis this morning. Those spiny appendages are like little strips of paper.
I'm going to suggest Mammillaria plumosa. I'm finding most of the cacti with a dense cover of white spines manage pretty well in the sun. I'm thinking the white reflects some of the hot sun away from the plant. M. plumosa is pettable. If it hides wicked spines in the feathery covering, I've never managed to get pricked by it. Mine has just sat there this year ?? but seems perfectly healthy.
Here's a succulent. I believe it's Sedum album. It hitchhiked in year before last hiding in another plant. Others may warn you off, but so far growing it is a pleasure. It's hanging from a tree limb now, but when it was tiny after I pulled it out the plant it came with, I kept it in a tiny 1.5" plastic container in all day sun. It should have cooked many times over because I'd forget it for weeks. It would get bone dry and the wind would blow the pot around. Occasionally it fell out and when I'd notice I take the hard root ball and put it back in and give it some water. I tried to hold it in place with stones, but the wind here competes well with those kinds of efforts so the process was repeated. When fall came I put it in a 4" container, but I still kept forgetting it so when winter was in full blast it was down in the teens F when I remembered. Nothing has fazed it. This spring I repotted it and hung from a tree limb and this is what it's done with a bit of care. I'm enjoying it a lot. This morning:
Another succulent. This is one of the Medusa type Euphorbias. I think either E. esculenta or E. inermis. One arm had tiny yellow blooms this year which might clear that up, but I haven't checked. I've grown this in all day sun. It did fine, but the side which faces the south track of the sun turned dark. I rotated it, but it would still tint up where the sun was blasting on it. I moved it and it's hanging under an oak tree simply because I prefer the greener look. I also gave it a bit larger pot. Baja said for several seasons that it looked underpotted. I think the growth was being held back maybe, but it stayed healthy. It's grown this summer with the extra room.
This is Parodia leninghausii, commonly sold as 'Golden Ball Cactus' (it was a ball when first purchased). It's not really spiny. More like coarse, gold hair. I've had it a long time. I've actually managed to acuire two more one of which was sold under another name that was a synonym. I've grown this one for a few years now and it has managed everything except a hail event quite well and even that wasn't a major setback. It's growing in an 8" container now, but it started out in a 6" clay pot for several seasons. I try not to leave it out when it's going to freeze, but it's been exposed to the upper range of the 20sF a couple of times without any ill effects.
I could show you some more that have spines, many of which are minimal and some I consider manageable simply because there's no need to be handling the plant and they go a long time before they need repotting. If you'd like to see those, I'll do it. As an example I'm going to show you one of them. One you possibly could leave outdoors all winter if the container could handle freezing temps. That would be Escobaria sneedii. Mine is in a stone container which is fairly heavy. The sun and heat apparently mean nothing to this plant. If the cold is extreme I'll move it where it has some protection and I've covered it when it's cold and wet just to keep it dry. Sometimes that covering has occurred after it's already gotten pretty wet from rain or snow, but it kept it from being continually drenched. The cavity in the stone is prox. like a 6" container.