Here's some information from an old article in Gun-Tests.com article - 1996. Yes, the annealing temperature is the same for all brass cases. I provided this because it discusses the proper temperature ranges.
Quick, uniform, consistent application of high heat is the key to good annealing. When the brass around the mouth reaches a temperature of about 660 to 665 degrees Fahrenheit, its surface becomes light blue. This is as hot as you want to let it get. If you let the color run too far toward the other end of the case, you can ruin the head by making it too soft. If you let the color on the neck go beyond light blue, and the shine disappears, you’re on the edge of ruining the case, and you may already have gone too far. If you let the case get red, it’s a goner.
But depending on getting the color just right is too loose and iffy to suit me. I prefer and recommend relying on something more dependable than personal color perception. The most reliable case thermometer I know is a 650 or 660 degree temperature-sensitive crayon called a temp stick. I’ll describe how to use it in a moment.
The hot, small flame of a torch is the only heat source you can rely on to give you the quick, local heat you need for selectively annealing the neck without heat-softening the base. High heat brings the neck and shoulder up to annealing temperature quickly, while the base end is still safely cooler; lower heat lets the base end get too hot while the neck and shoulder are getting just hot enough. Therefore, safe neck annealing takes high heat and a surprisingly short time.
Temperature-sensing crayons allow close temperature control. Any well stocked welding supplier has them or knows where to get them. McMaster-Carr stocks two kinds, and I hope a few handloader suppliers like Huntington’s will stock them if there’s enough demand for them. The mark made by one kind of crayon melts at the rated temperature, plus or minus one degree. The other kind leaves a yellow mark that changes to red-brown at the rated temperature and tolerance.
The 650-degree crayon, which melts at about 10 to 15 degrees below annealing temperature, is Number 3261K449 in my old McMaster-Carr catalog, at a nominal price of $7.80. Be sure to specify crayon when you order. McMaster-Carr also sells 650-degree temperature-sensing pellets under the same catalog number. These pellets are for other applications and aren’t adaptable to case annealing. The 660-degree crayon changes color at approximately the correct annealing temperature (within 2 degrees or so). Its catalog number is 5960K71 and sells for $6.20. Both come with aluminum pocket holders.
Which crayon is better? For annealing only a short area such as just the neck and not much lower on the case, the 660-degree color-change crayon is probably better. When the color changes a bit lower down, the upper neck should be just about the right amount hotter. Annealing a longer area means there’s a wider range of temperatures between the mouth of the case and the lower edge of the annealing area. The 650-degree melting crayon allows a range of about 10 to 15 degrees Fahrenheit. You could use this crayon to mark the lower edge of the area to be annealed, or the other crayon to mark the upper portion of the annealing area.