sun Transplant Shock: Leaves are wilting after putting in SUN | HELP and SUGGESTIONs needed for tiny sur

Hi All,
 
I have transplanted my chilli pepper to individual pots. Its being 2 days and I tried putting them in sun. But seems most of leaves started wilting after 2 hours of sun. Below pic is when they were standing upright and i just kept. After 2 hours and some stem and leaves started wilting/drooping. I will post wilted pic later as am in office.
Please help with your suggestions on how can i keep those tiny life back.  
 
Any help/suggestion would be appreciated.

They'll be okay, just keep them in the shade and don't overwater them. It's pretty hard to kill a pepper plant. 

I doubt it is transplant shock.  Plants started under lights or even in a window can not tolerate direct sunlight.  It is kind of like your own skin in the spring, gotta build up to it or you will get a sun burn.  But after you have built up to it, no burn.  If you move them back to where they were and make sure they arent too dry, you should be fine unless they were out too long.

If you search for the term "hardening off" you will find lots of different methods.  For hardening against sunlight, all I do is put them in ambient light for a couple weeks and then they are good to go.  I use places like the car port, barn doorway, and anyplace they dont get direct sunlight.  Works great and I am lazy so I dont like moving them around.

little of both , transplant shock &  not hardened off ,   

Easy hardening off method,for me.
 
I don't mess with shade for X amount of time.
Too hot here,root growth I think is my main problem.
 
I grow all starts,from seed, in 4 1/2 in. pots.
I sprout seeds in 2 1/2 in. zips...
 
I found that root mass was my problem AFTER I used to harden off my plants in the shade.
Had to baby plants too much=water 2+ times a day or perfectly grown starts cooked in the heat...
 
I found that putting plants directly in #15 (7 1/2 gal. pots) worked best(from 4 1/2 in. pots).
Tall is the key,need only a couple hours of real sun a day to harden off.
 
The white lined (inside the can) work better than the gold or silver cans.
 
Big pots allow a few weeks of extra root growth.
 
The trick is to put a can (1 gal.+)with the top and bottom cut out around my starts,
Cardboard box or anything a couple/4+ in. inches taller than my plants.
Make whatever you use somewhat tight fit.
 
This way my starts get pot/root space to harden off + indirect sun to harden off plus lots of pot space to keep up with supporting the plants..
 
Less work etc.
Shade cloth sucked,too much shade or not enough...
 
Shade cloth also let the smaller nasty bugs in,but the bigger good guys couldn't get in to help me out by eating them...
I don't use poison!.
 
Hands aren't working today.Health stuff...
 
I'll answer questions latter when I can.
 
Your pic looks like perfect candidates for my method.
No offence.I never have starts as skimpy/leggy as your pic.
Use more Lumens of light.