I wanna try to make a bulgarian helm from 13 century from one whole piece.
and i wanna ask few question, if this is a the right section(if is not sorry for my misstake)
1) How thick should a sheet(with carboon in it) - i know she must be 2mm thick but i want to make it at least 3mm
2) Is it compulsory heat treatment

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It depends on what you're going to use the helmet for.
I'm going to assume it's for reenactment, so in that case 2mm would be perfectly fine. 3mm would be a bit too thick.

I'm not really sure there are Bulgarian or Balkan, Byzantine, etc helms from that time that are from one piece, although you could possibly interpret an image or two that way. The majority of helmets that appear in Orthodox art are composed of multiple pieces, with the exception of the 12th century Skylitzes chronicle - but given the size and detail of images there I would be wary of it's depictions, and would go with a more detailed source.

However, the image you've attached is that of a cervelliere - a type of helm that was popular in Western Europe and the crusader states at that time (and a couple of centuries later), but somewhat different from what you see in Orthodox art from the period.

In addition - if you haven't got experience in armour making it would be much easier to go for a helmet constructed from multiple parts. Also if you get something wrong it will be easier to start a single part anew, rather than the whole helmet.

If you're aiming for a late 13-th century Balkan soldier you could also go with a simple kettle helm, although it will be a bit more challenging to make than a brimless helmet.

You don't need heat treatment, however if you go for the one piece route, you would need it otherwise the steel just might not take it.