I have successfully removed candle wax with the warm iron method.
First you put an ice bag (or just ice in a plastic bag) on the stain to make
sure that any wax there gets hard. You almost nearly freeze it. Do not get
the carpet wet.
While the wax is still "frozen," very gently scrape the wax away with
something that has an edge but is not sharp. (I think I've used the reverse
end of a regular spoon.)
Then get some absorbent **white** absorbent paper---paper towels that have
absolutely no pattern are excellent. **Do not use colored paper!" Use
several layers. Using a very slightly warm iron, press the paper towel over
the spot. As grease is absorbed, continue moving the paper towel so that a
clean paper towel is always under the iron. Stop when you think the carpet
is getting too warm and let it cool. Then begin again and work until all
grease is removed.
After that, I can't remember. Seems to me I might have used a cleaner's
solvent to dab the area. But I'm not sure about that part. Someone else,
please fill that part in. Whatever you do, just blot the spot with the
cleaner; do not use a rubbing motion.
However, in one spot I got the wax out, but it was a red candle and the red
stain remained. Even a professional couldn't get it out.
Best of luck with this task----