You can tell the steel is too hot if it starts giving off " sparks ". THat is the carbon in the steel burning off, a definite " No-No". When you use some kind of oven, or enclosed container when heating parts, this is something you want to keep an eye out for. Remove the part from the heat AND from the container- as it takes the container time to lose the heat, too- until it cools down to the right temperature. It never hurts to have a magnet around. Just check the metal when its cold to see if it really contains iron, and attracts the magnet when the metal is cold!
Don't skimp on the depth or amount of oil you use to quench. A large 1/2 gal. container with a quart of oil in it can be help plenty close to your heat source to get the frizzen from the heat to the oil while the frizzen stays at temperature. As thin as a frizzen is, it still is steel, and it hold heat fairly well. It is not quenched in seconds. It needs to be swirled around in the oil for at least a minute, and then left to continue to cool for a few minutes more before being removed. Turn off the heat source. Air out the room, Go get a breath of fresh air, get something cool to drink. Then, go back and remove the frizzen from the quench.
The frizzen will have a scale on its surface that is gray-black in color. You can remove it with emery cloth backed with a file. I like to use a half round file to back the paper to polish the face of the frizzen. The backside and the base of the frizzen can wait. Inspect it for cracks. hold it through the pivot hole on wire, and strike it lightly with a piece of metal to hear how it sounds. It should give you a high pitched " ting ". Using a very small jeweler's file, test the back of the frizzen to see if you can remove any metel. If its truly hard, a file will not cut it easily.
Then go to the tempering process using your oven. When the frizzen is tempered, then you can remove the scale from the rest of the frizzen. DO NOT SKP THE TEMPERING PROCESS.( The shooting of the gun may never break the frizzen, but if you bump that frizzen hard enough against something, or the gun falls over and hits a rock or concrete, it may break the frizzen. )
If you have a power grinder, get one of the wire wheels and use that at high rpm to remove the scale. That seems to do it the fastest. After its tempered, you should be able to file it, or polish it with emory cloth. to final finish.