Well we make a crap load of that style hawk in a coal forge so I'll see if we can help..First the wrap&weld method making hawks and axes is the most traditional way..Historically wrought with a high carbon bit..Anyway if your using 1045 is wont take that much heat..
Lets start with your fire....
*You need either a beehive fire or a large deep fire..At least 4" of coke between the tuyere and the work piece..Then you need a couple of inches of coke above the work piece..
* The steel needs to be cleaned, brush all the forge scale off..
* We use 20 mule team borax for flux.
* The color, hard to explain but a high yellow of what your working with..Look for a glassy wet look to the surface.
*Make sure your whole work piece is brought up to welding temp..Thats where most folks bugger up a wrap&weld hawk..They wont bring the whole head up to heat and the eye wont weld right.
* Light taps, start at the bit and work your way back to the eye..Your not trying to kill a hog, just set the weld..
*Do two or three welding passes before you start to form the eye..Make sure the eye is welded right or it will split open when you use it..
Heres a few pics..Heres a head ready to weld up..
Here it is after the first welding pass..
Here it is after some shaping.Work at a high heat when doing this...A lot of folks will say "you can upset" a welded piece but you can if its welded right..
Heres a big deep fire..Notice a hawk head in there right now..Its already been welded. Its being hsaped at this point..NOTE..When your welding it up your hawk should not be visible like this..
Heres a wrap&weld style head. You can see what it should look like in front of the eye after clean up..