I don't know about "the procedure", but a procedure I have used is
Using 0.08% Carbon 0.010" thick shim stock.
clean and weigh 0.010" shim stock (or whatever thickness you are using). Weigh to nearest .0001 g (0.1 mg)
This is Initial Weight (IW)
place in furnace for 20 minutes
cool in vestibule under atmosphere to below 1000F
clean and re-weigh shim
This is Final Weight (FW)
The percent increase in weight is
(FW-IW)/FW * 100
But, the initial shim had 0.08% C so,
% C = ((FW-IW)/FW * 100) +.08
Note, generally, the carbon content of the shim stock is unknown, but relatively low, 0.06-0.08. We always used 0.08.
Note 2, we would typically use a 1" by 2" shim (approximate dimensions). IIRC, they nomially weighted about 2.5 grams.
Note 3, care has to be taken on cooling from temperature to prevent oxidation. We had shim vestibules built into furnace.
Note 4, the soak time doesn't really depend on thickness, but is just the amount of time it takes to come to equalibrium. We did trials and found 15 and 20 minute shims to be equal, so we settled on 20 minutes. ymmv.