Straighten Permed Hair
A: Given that the perm service changes the chemical side bonds in the hair, and that these changes are pretty much only affected by chemicals that can undo the process (the same ones that created the curl), you should still be able to use physical styling methods to straighten the hair without negative effect so long as you make sure to protect the hair from damage.
Moisture-rich shampoos and conditioners, with deep conditioning treatments every several days are imperative. In addition, you should be using leave-in conditioners and protective products designed to protect hair against heat styling damage.
Then come the tools used. If you don't have one already, get yourself a flat iron with an adjustable heat setting (something more than high-medium-low). You need to be able to finely control the heat of the iron, so that you use as little heat as necessary to get the results you want. I also recommend an iron with ceramic features. It will help to smooth the hair better than metal plates - even those that are coated.
The secret is to start with the very lowest heat setting (certainly not hotter than 1/4th of the possible temperature) and do test passes on the hair. Keep increasing the temperature in small increments until you reach the level of heat that smoothes the hair to your liking. It is better to make a few passes with a lower temp than one with too much heat.
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See also:
How perms work
Heat styling basics
How to style hair with a flat iron
Will using a flat iron on my permed hair affect the perm at all?