As a natural, one of the things I can not seem to get a hold of yet is a silky wrap with NO HEAT involved. Oh my, once I get that down, I am good to go as far as getting rid of the heat. Anyway, I came close with something similar.
This style was done with no heat. I washed, conditioned and oil my scalp and ends, wrapped the hair overnight with a scarf and let it be. The next day, my wrap came out sooooo nice and soft and also straight. I had also put in a few rollers for the twirly curls. I loved this effortless hairstyle.
Give it a try.