Have you tried any of the non-damaging ways to straighten?
1. Dampen you hair and separate into pigtails, wind a long ribbon around the length of each pigtail and tie at the end. This keeps the hair straight whilst it dries (this one gets the best results for me and is easiest and is comfortable to sleep on)
2. Make your hair damp. Tie your hair either into a ponytail or pigtails and continue to tie lots of hair ties at 1-2 inch gaps down the hair. For this to work the hair must become "stiff" - ie when you lift it at the top of the ponytail the rest must move without being floppy. (This sometimes works for me and sometimes doesn't)
3. "The Doobie" - Wrapping your hair around your head, effectively using your head as a giant roller (see video youtube.com/watch?v=G5BzYBME06Q for wrapping technique)
4. If you can get hold of some really big rollers (Over 3" diameter) these should leave your hair straight, although I've never been able to find any this big. To minimise damage try not to use the ones with velcro as these aren't good for your hair.
5. Some people have success just putting their hair into a non-twisting bun whilst damp and leaving to dry (this doesn't work for me though)
I think there's another method but I can't remember it!
To get the best results it is important to make the hair damp first as this breaks the hydrogen bonds that form whilst drying which give it it's curly or straight shape. I generally do these overnight, using a spray bottle to make my hair damp but no so wet that it won't be dry by the morning (although this wouldn't be such a worry if you don't have thick hair).
I've never got absolutely perfect results with any of them but my hair is curly and I can get it reasonably straight hair so if your hair is straightish to begin with you might have more success (I know people with wavy hair who get brilliant results - I think my hair is just too curly!).