We definitely need input from wood scientists or material engineers.
Anyhow, according to my "primitive" speculation,
it appears that deep heat treatment should be
around 175°C (347°F) at the minimum and
about 230°C (446°F) at the maximum.
But charring the wood will damaged the stave.
Cf.
https://bioresources.cnr.ncsu.edu/wp-content/uploads/2019/02/1965.1.555.pdfSynopsis - The thermal softening of isolated samples of lignin, hemicellulose
and cellulose has been investigated by observation of the thermally induced
collapse of a column of powder under constant gravitational load. Softening
temperatures of lignins ranged from 127-193 °C. Birch xylan and pine glucoman-
nan softened at 167 ° and 181'C, respectively . Sorption of water by lignin and
hemicellulose caused pronounced decrease of the softening temperature-in
some cases, to as low as 54°C. Softening points of both dry and moist lignins or
hemicelluloses have been shown to correlate with the temperature at which the
sample develops adhesive properties. The softening and adhesive behaviour has
been explained in terms of the concept of the glass transition for amorphous
polymers. Sorbed water is considered to act as a low molecular weight diluent
in plasticising the polymer chains and lowering the glass transition temperature .
Celluloses were found to soften at temperatures greater than 230 °C. In contrast
to lignin and hemicellulose, sorption of water by the cellulose had negligible
effect on the softening temperature . This difference was probably due to the
crystalline nature of cellulose and indicated that water did not plasticise individual
cellulose chains at the molecular level .