What have you planted before? There are lots of vines that actually seem to like the heat! Here's a few:
Cat's Claw (Macfadyena unguis-cati) beware--invasive!
Orchid Vine (Mascagnia species) may be hard to find
Snail Vine (Vigna caracalla)
Pink Trumpet Creeper (Podranea ricasoliana)
Hybrid Trumpet Creeper (Campsis x tagliabuana) also invasive, and deciduous
Queen's Wreath (Antigonon leptopus) deciduous
Remember that any plant in a hot location like that is going to need deep, infrequent watering--two feet deep every 1-2 weeks--to help keep the roots down in the cooler soil zones.
Hope this helps! : ])

If it's a west-facing or south-facing wall, it may just be too hot. We (in Tucson) have east-facing walls painted white and its amazing how hot they get. You could try a trellis set away from the wall. I like Queen's Wreath and it is very heat tolerant.

I've tried passion vine, hall's honeysuckle, jasmine, pink trumpet vine, snail vine, and lady banks. Right now I'm trying a Red Riding Hood Mandevilla. It's been there two week and is not looking to good. I've dug up the soil all around where I'm planting them and mixed in some compost, then put a little compost on top as mulch. When I first plant I water every other day for the first week, then go down to twice a week, then down to once a week, always slow deep watering each time. I'll be looking for some of the other vines you've mentioned and give them a try, I have a lot of block wall to cover. The wall I'm trying now with the Red Riding Hood Mandevilla is a west facing wall so gets pretty hot. Let me know it you think I should move the vine and try something else there.

Thanks for the help,
Gemfire

Hi Pam,

I have lady banks, rogers red grape, and coral vine, all planted directly against south facing walls.

It really sounds to me like your watering schedule is trying to get them established quicker than they can. Young plants in our summer will need watering more than 1x per week unless it's a xeriscape plant- especially if you've amended well around the root ball which aids drainage. It can take up 2 years for a non-native plant here to develop a good deep root system.

I've personally never heard of anyone getting mandevilla to thrive here under any condition and wish to heck all those big box stores would stop selling them. I would plant something else. We at one time had lady banks against a west facing wall and it did well, be careful though, it gets huge and needs tons of space. I think you should try the Roger's Red Grape myself, Baker's usually has them. You can anchor wires to the wall and have it go whereever you please. Is deciduous.

I have some bougainvillea (the vines, not the bushes) and the orange honeysuckle (is that what they're called?) both growing against south and west facing block walls.
The heat did a little damage to a couple of the honeysuckle, but nothing permanent. It's actually extremely random as to which of the plants seemed negatively affected by the heat. I'm still trying to figure if those just didn't get quite as much water as the others.

Passion vine doesn't often work on a south or west facing wall. Hall's honeysuckle can work, but it often gets stressed and ugly in the summer. There's no species of jasmine that will work on a hot wall. Mandevillea needs a northern exposure, preferably with a couple of feet of overhang to shade it midsummer, and it's often too finicky to live even there! Pink trumpet vine, snail vine, and lady banks' rose should have all worked, however.

Here's a few tips for starting plants in hot spots:
Don't mix in too much organic matter when planting: best proportions are 1/3 mulch or compost to 2/3 native soil. The heat of summer can turn a heavy layer of organic matter into an underground compost heap, releasing toxic gasses that kill roots. Adding a little sand to the mix will help improve drainage without increasing the risk.
Make doubly sure not to plant too deeply: the top of the original root ball should be at, or 1/4 inch above, soil level when you are done planting. Soil piled around the stems kills the bark and keeps the sugar the leaves make from reaching the roots. Eventually the roots starve to death, and that happens very quickly in the heat.
Do put a 2-3 inch deep layer of coarse mulch or ground bark on top of the ground after planting to keep the roots cool and conserve water.
Reduce watering frequency veerryy gradually! What's worked best for me: water every day for two weeks, at least one gallon per container size number--5 gallons for a plant from a #5 container, etc. Then 1 1/2 times as much water, every other day for 4 weeks. Then 1 1/2 times as much again, twice a week, for 8 weeks. Then 1 1/2 times as much again, once a week, for 16 weeks. Then 7-10 gallons for each yard of spread along the wall, once every two weeks in the summer, and the same amount every 4 weeks in the winter.
If you have sandy soil, you might have to water twice as often.
Good luck, again! : ])

Wow! I didn't know anything would grow on those ugly block walls. Luckily for me mine faces east so perhaps I'll have better luck than some? I really hope something works because those walls are ugly as sin and I can never seem to do anything with them. Everyday I wish I had a chain-link fence. Hello instant trellis. *sigh*

I have a friend who tried to grow Queen's Wreath because she heard it was heat tolerant. She never found out if it was because her chickens ate it :)

I'm having the same problem with the West facting wall. My Lady Banks roasted and then toasted this summer. I might try Pyracantha. Would that work?

How do get rid of cats claw? And, what would grow in it's place, in a totally shaded spot on a wall?

Mandevillia will NOT survive in Phoenix without really special pampering.

Whatever you plant:
You have to start the plants in the fall, so they have as long as possible to establish a root system.

You might have to give some supplemental shade until the plant is a couple of years old - one way to do that is to plant a rampant sun-loving annual vine like Armenian cucumber

They will need slightly more frequent watering, good mulch, and careful monitoring until you figure out that particular location.

I'm going thru the same problem. My nursery girl suggested some trees with dappled shade; know they will take time to grow, east of the wall, to give some protection from the hot afternoon (west) sun, at which point she says we could then plant the wall solid with vines. Don't know if this is an option for the way your yard is situated, but seems to be our only choice. Tried everything there as well, and all fry sooner or later. And it will give some shade to us as well on that side.

I have bougainvillea on a south facing wall that pretty much gets full sun year round and it does fine. I've also seen pyracantha growing on a south facing wall for years with no problem, I grow my armenian cukes on an east facing wall with full sun during summer and it grows great. Also seen luffas grown like this.