I am trying to root my UC Davis cuttings and I have them outside on the porch during the day and indoors under plastic at night. They get less than an hour of very early morning sun filtered by 70% sunscreen and then only reflected light (total shade) the rest of the day. They get sprayed every few hours and don't seem dried out at all. My humid monsoon season kicked in just in time to chance having them outside. My porch gets up to 105F on days we go over 110F and I am starting to think they should be brought in during the extreme heat of the day.
Thanks for the help

Neglect half of them.  Leave half outside all the time (even at night).  Don't water them unless they get dry.  

Baby the other half, bring inside when they look sad, etc. 

Then see if the ones you neglected do just as well as the ones you baby.  I bet they probably do.

Temps over about 85 decrease root function so I'd try to keep them under that but over 75 most of the time.  If you put them outside in the shade move them into the sun as soon as you see the tiniest of green bud but continue to shade the below ground part.

You can put cuttings in refrigerator(vegetables container）for one week, not spray water. After one week place them in place with 25 degres celsuis.

As an experiment I took 6 fig cuttings and placed them in clear plastic cups in a mixture of 50% perlite and 50% potting mix.  These were bare cuttings with no root development at all.  I watered them in really well and stuck them outside on my deck underneath a bench seat.  They get ambient light but no direct sunlight.  They've been in the cups for about 2-3 weeks now and all of them have 2-3 leafs and have a few visible roots against the insides of the clear cups.  They've rooted wonderfully.  in another week or so I'll probably move them to larger pots and start exposing them to a little morning sunlight.  

Jarl, I do the same here in Maryland.  I think the answer is straightforward for the Eastern part of the U.S. coast, where temperatures rarely exceed 95 for long.  Just stick them outside in the shade and they'll do fine.  However, in the hot and arid west, such as Arizona, where temperatures regularly get well over 100, the answer might be different.

rcantor is correct. Anything over 85 degrees is not very helpful to the trees. Try to give them as much morning sun as possible, My UCD cuttings get an hour each morning through wooden lattice then shaded all day and then about 30 min. of late evening sun and they are rooting very nicely, but try to keep them at 85 degrees and out of the sun during the heat of the day. You may want to consider growing under shade cloth with those high temps once your cuttings get potted up.

If 105 is the maximum temperature during the day and the pots are completely shaded and moist, I wonder what the average ambient temperature during the day would be in the actual root zone?  Must be less, but how much?  What if you buried the pots in soil?  Maybe that would help to moderate the temperature of the root zone. 

For me the best plan is the one that works and takes the least amount of maintenance and intervention