Submerging in water will get water in places that won't dry out until you have that same warm sunlight you don't want to wait for! It will also want to shrink the material although not a huge amount.
A hair dryer will work but will take considerable time as you need to heat the curtain as evenly as possible and maintain that heat for some period of time for it all to actually relax. Lastly, be certain to NOT create any hot spots in the window or it can distort it in a manner that is irreversible.
If you have a heat resistant flat surface to lay the curtain on, try blowing the hot air between the surface and the curtain. Do so from different sides of the curtain to avoid overheating one area. The heat will not only distribute somewhat evenly but will heat both and hold that heat in. Keep in mind that something like a laminate counter top is NOT exactly heat resistant. The accumulated heat can permanently break the bond of the adhesive thereby delaminating it!
Some of these issues may be insignificant depending on the condition and fit of your curtains but should factor into your decisions.
