Nope, doesn't work that way. Merely heating a frizzen in hot coals would only soften the frizzen. In addition, the leather needs to be charred, so's the carbon from the leather can migrate into the steel of the frizzen.
The best way to harden a frizzen depends on the make of the lock. American made locks, Chambers, Davis, and L&R are made of 1095 steel, which is a through hardening steel. Foreign made locks have case hardened frizzens, which need to be heated to a bright red-orange in a carbon rich environment, then quenched in water.
Place crushed charcoal, about the size of pea gravel, about 1/2-1" deep in a steel container. Place the frizzen into the container and fill with charcoal. cover the container with a loose fitting lid. Place the container in a hot fire to cook for a coupla hours, keeping the fire burning hot enough to keep the container to a red-orange color for two hours, or so. Longer is better. Pull the container out of the fire and dump the contents, frizzen, lid, and glowing charcoal into a 5 gal bucket of water. I do suggest wearing good leather gloves, a face shield, and stand up wind of the bucket.
Test the frizzen with a dull file. If the file skates, instead of cutting the steel, temper in the kitchen oven at 350 degrees F for an hour. Use two good oven thermometers to gauge the real temp of the oven, since some oven thermostats are off as much as 100 degrees.
Once the frizzen is tempered, polish it up with 280 or finer paper and holding the body of the frizzen with pliers, heat the tail of the frizzen to a full blue, with a torch. Heat it slowly and allow the colors to run up the tail and almost across the pan cover. Quench the frizzen to prevent the colors from running onto the face of the frizzen, which will over heat the bottom of the face of the frizzen, making that area a little too soft.
Or you can just heat the frizzen covered with Kasnite for as long as you want to hold the frizzen in the flame of an acetylene torch, quench in water and temper as above.
The same basic instructions will harden an American made frizzen, but just heat the frizzen with an acetelyne torch or in a hot fire. No container needed. Then quench in light oil. Canola oil works pretty well. Temper as above and you should have a hot sparking frizzen.
A search should turn up more information.
God bless