For very thick hair, you need to curl very small sections at a time...it will likely take you and hour or two to curl her hair. Don't spray it while on the iron, that will just promote burning, but after you get a section done, spray it.
Section her hair off into three or four layers, pulling them up with clips. Curl the bottom layer (near the nape of her neck first) in VERY small pieces, then when you have the whole section done, spray. Then let down the next section/layer and repeat.
Alternately, and what would work best, would be to shampoo her hair early the prior afternoon, put her hair into sleeping curlers (I have a type for my daughter that are really just a strong pipe cleaner surrounded by padding and material) and have her keep them in for the remainder of the day and overnight. Don't take them out until the last minute...that will usually curl my daughters straight, thick hair beautifully and without the heat. It works best when you do it wet and leave them in for at LEAST 12-18 hours, though.
Pull it up last, regardless of what method you use.
Ah, the joy...my hair is naturally curly. ;)