Answered[ Edited ]
I have to say... I don't think its possible to straighten curly hair overnight and especially without any heat products! I have wavy curls myself and use a blow dryer and flat iron to keep myhair smooth and straight but I'm honestly not familiar with any ways to keep the hair straight without using heat. You can try putting damp hair in braids that will give you softer waves that will dry over night, or add a straightening spray/serum or shampoo and conditioner but most of those do work best with heat.
You may even want a chemical Keratin based or Brazilian straightening treatment that will keep your hair straight for weeks.
I'd recommend doing an internet search for some more hair tips as there may be some I just don't know about and am not familiar with!