500 is better obviously that 800,,
Also, though I've read that a 500/550F temp range will produce a blue finish using the Carbonia method, I was never able to make it happen at that low a temp. I'll be the first to admit my experience with the Carbonia method is far far less than the Charcoal method. But 500/550F didn't produce anything but a grey hazy cast to the metal.

Perhaps others doing the process with more time & experience have developed the necessary technique to tease the blue color out at the lower temps. It would surely be advantageous to run the parts at that temp as opposed to 800F if you could avoid it esspecially when dealing with critical parts like frames, barrels, etc.

Older descriptions of the method often mentioned varying the temp during the process and lowering it at some point to around 600F IIRC and back up again. Everyone using the process surely developed their own little techniques and tricks for getting good results. It's the same with case coloring.

So much depends on what steel you are dealing with and exactly how it is supposed to be delthandled with as far as it's hardening & tempering qualitys go.
The time @ the drawing temp means alot (soaking ), quench or slow cool down, any temp variation needed during the soak, etc.
They are not all a simple 'heat it up and quench makes it hard,,,heat it a little draws the temper'. Some demand some fairly sophisticated equiptment and procedures to get where you want to go. Vacuum furnaces, salt baths, etc are some of the things sometimes necessary to properly deal with some modern steels in heat treating.

A quick story....
I will never forget the 'one-of' shotgun proto-type,, finished, in the white but still soft. Needing hardening, the owner/mfg asked if a certain C/C/H person could harden it. "No Problem,,I'ts all just iron" was the confident answer. "It all goes in the same furnace".

Not wanting to listen to someone else with machineshop experience that offered to gather proper heat treating info on the steel type, which was provided by the mfr,,into the furnace it went.
It came out looking like a giant pretzle from the County Fair and no case color other than a bit of blue against a grey back ground. The color was actually not a problem as it was going to be polished back to a 'french grey' but the contorted parts were.
Again,,"not a problem",,,as the twisted forend iron was tightened into a bench vise. A couple of educated taps and push here and there and it'll be all back in place. The sharp snapping sound like an icicle breaking off of a roof on a cold January morning told another story. No attempt was made to straighten the action and side plates.
Moral: Know what you're dealing with before proceding....