The adiabatic flame temperature for a stoichiometric Propane/Air flame is usually given as 1980 degC, 3596 degF.
We do not see this temperature in forges for a number of reasons.
First is that we cannot achieve perfect insulation and there will be some heat losses.
Second is that we usually need to run a reducing atmosphere in order to limit scaling and decarburization. We therefore add extra fuel.
At the stoichiometric ratio, the flame temperature is high enough to cause some Oxygen to react with Nitrogen and produce highly reactive Oxides of Nitrogen. There is also unreacted Oxygen present which has not had time to combine with the fuel. The Oxygen and Oxides of Nitrogen readily react with the workpiece at these high temperatures and will quickly ruin it.
We can reduce the flame temperature either by adding extra air or by adding extra fuel. Most processes are only really concerned with heat release and temperature and will run lean (with an excess of air). Air is free and fuel is expensive, so it makes sense. By completely Oxidizing the fuel, all the available energy is released and a minimum of poisonous Carbon Monoxide is produced. By adding enough extra air to get the flame temperature down to around 1000 degC, 1832 degF, very little Oxides of Nitrogen are produced.
For forging, running with excess air would mean that there is a lot of unburned Oxygen at the workpiece. This is extremely undesirable (scale, decarb) and is the reason we run rich (excess fuel).
We can vary the amount of excess fuel we add. Adding more excess fuel reduces the flame temperature and makes the forge atmosphere more reducing. We generally want to use the most reducing atmosphere we can (for minimal Oxidation), consistent with reaching the desired temperature in a reasonable time.
I use Amal atmospheric injectors on my burner: British-made commercial Venturi mixers with a very finely-adjustable choke. This gives very fine progressive control over the fuel/air mixture. I use the version factory-jetted for Butane, even though I run on Propane, because the Butane jet is slightly smaller and will reach a higher temperature than the factory Propane jet when the choke is fully open. A number of British smiths I know have taken to using them because they provide all the adjustability of a well-put-together blown burner with the freedom-from-electricity of a Naturally-Aspirated burner.
The highest forge temperature I have measured (using a Platinum-based Type S thermocouple) is 1554 degC, 2829 degF, with the indicated temperature still rising. I am sure it would have gone higher, but I was reluctant to risk the expensive thermocouple and it was already above the melting point of Iron. There was still visible Dragons Breath, so I am confident the forge was still running rich at the time.
By simply choking down the air supply, I could run the same forge/burner combination at any desired temperature down to around 760 degC, 1400 degF. At this, much lower, temperature Carbon (soot) was being deposited on the workpiece. Huge amounts of poisonous Carbon Monoxide were being produced and there was no visible Dragons Breath. I surmise this was because once the partially-burned gases mixed with air outside the forge mouth, the temperature was too low to sustain combustion.
In essence, you can run at any temperature you might reasonably want to run with a reducing flame, if you have good adjustment. It is "just" a case of balancing the temperature needed against the reducing-ness needed and finding the best compromise.
It sounds like your air:fuel ratio in PID mode was enough for the flame temperature to exceed 1950 degF and to hold that temperature by cycling the hi-burn. You then adjusted the air:fuel ratio to give a reducing flame at "about" 1885 degC.
Are you running a blown burner or Naturally-Aspirated?
