Is flame temperature and the temperature above the flame about the same?

This is a practical question that looks not that academic.

I'm trying to design an integrated forge that can do heating and forging together. Blacksmiths usually make a forge kiln like Figure 2, as the air will be pumped in to provide more oxygen to the chemical reaction. I wonder if the coal surface, or the flame, and the air above the flame has the same temperature so that I could transfer the hot air to the anvil through a well heat-insulated pipe as Figure 1 shown below.

Sorry for my terrible graph, I don't have a graphic tablet :P

From daily experiences, we're really safe if we just keep a little bit distance and won't get hurt by the fire, because the heat energy of the fire is spread to the surroundings. My idea just seems, well, just seems not established.

I wonder if this hypothesis is true: Oxygen participates the reaction and the air should gain the heat the most first, meaning the air input just being heated to the flame temperature, and if it doesn't lose heat then it will keep the temperature in the pipe to the end of the pipe.

Furthermore, though if the temperatures are the same, will heat up by way in Figure 2 faster than figure 1? One of my another hypothesis is that oxygen molecules first react with carbon molecules and transfer the kinetic energy directly to both iron molecules and nitrogen molecules, and then the iron molecules transfer kinetic energy to the nitrogen else in the air, as the average temperature is the same but way 2 will gain temperature faster.

I'm TOTALLY not sure any of my hypotheses are right, and I don't have space to do the experiment safely, so I feel my hypotheses are fairly lacking explanations and I wonder if someone can tell me whether my design is practical :D

• Could you clarify what you want to heat up faster? Otherwise the only thing I can think of right now is that the heat equation has thermal conductivities in it, perhaps check some thermal conductivity tables... – Emil Oct 25 '18 at 22:00
• @Emil Metals, iron most often... well blacksmith do stuff with iron. – iry Oct 25 '18 at 22:06
• I have my doubts that the hot air at the anvil can do the job. There is a LOT of radiant heat given off by the coals. That radiant heat will not be given off at the anvil in your proposal. Of course, there is one way to find out, and that is to build the new device and give it a try. – David White Oct 25 '18 at 22:52
• The atoms are hottest (most K energy) just after they react and because they are so hot they transfer their energy to any other atom that is just hanging around (like nitrogen) so that means the original atoms are getting cooler. The further away the more atoms have interacted and the average temp will decrease. In theory you could feed in pure O2 but the pipe you propose may melt, too hot to handle!? An acetylene welding torch is always kept close to the metal. – PhysicsDave Oct 26 '18 at 0:39