Methods for producing devolatilized and/or activated carbon in a reactor or reaction vessel of a heat treatment system from a suitable carbonaceous feedstock by introducing the feedstock into the reactor tangentially at a rotational velocity of at least 90 RPM. The methods include the steps of providing a combination of conveying means and a gas flow having various compositions and creating distinct carbonaceous feedstock material flow patterns and process conditions such that the feedstock is conveyed through the reactor or reaction vessel and heated via combustion, thereby producing activated carbon or other heat-treated carbons while concurrently avoiding adverse reaction conditions. Single and two-stage heat treatment systems may be used to heat a carbon feedstock, to which one or more industrial minerals may be added to co-produce compositions such as lime with the heat-treated carbon.