According to wig experts such as katie bair, the hot water method is the way to go for curling wigs.
Since artificial fiber wigs are essentially plastic, not hair a hair dryer will melt or deform the fibers. It's very hard to control the heat generated by a hair dryer and the fiber goes from soft to melt in milliseconds.
I have successfully used a steam gun (hard to find now) which is very similar to a steam wand they use to take wrinkles out of fabrics like silk but again you have to be really careful that the water is not too hot or that you are too close to the wig.
Another good method is to put hot water in a spray bottle and spritz it over wig hair on curlers. Let cool and see if the curls are tight enough.
Just as people have already said, it's best to use too cool of water and have to re-do it than to go too hot (like boiling) and melt it.
An old wig or one from a 2nd hand store is great to practice on too. That's what I do.
Hope that helps
Ja ne
Kato