Well I am not Mule Deer, but I am the former CEO of Cast Performance Bullet Co, and I have a lot of experience in reloading much of which is with handguns.
So I will give you a short easy way to do it and if Mule Deer has one to add, I am sure it will be good info too.
A candle is not going to add heat fast enough to the mouth to keep the head of the shell from also softening.
A red hot block of steel is very good but requires a heat source large enough to get it hot. You need only place the case mouth against a red hot block for about 1 second to anneal it and then drop the case in water.
The easy way to anneal case mouths of handgun brass is to melt a small pot of lead and bring it to about 675 degrees.
De-cap you brass and dip the case mouths about 1/2" deep into oil, and then about 1/4" deep into the lead holding them by the heads with pliers. Hold them in the lead about 2 seconds, and then drop them into water. The oil keeps the lead from sticking to the brass.
You then clean your brass normally and load.
For safety purposes, keep the water well away from the molten lead. If you want to create some excitement, put a drop of water into molten lead. You will be treated to an explosive event and learn the meaning of the term "tinsel fairy".
You may be blinded and badly burnt during this process but on the plus side, you are unlikely to forget the lesson soon.
When working with molten lead, always wear full protective gear, including full face mask and non-flamable clothing that covers all skin compleltely.
I often water drop bullets but keep the water well away from the molten lead, at least 10', with a physical screen between the water and lead.