To go along with Kutter's stated temps regardless of whether bone or cyanide is used "IF" the critical temperature of the steel is not exceeded no hardening takes place.
This passing of the critical temp is when warping can (& often does) take place. A part can be "Colored" at a temperature below the critical temp, "But" it will be raised to a high enough temp to draw all residual hardness from the existing part.
When the colors wear off the hard case remains unless it is drawn from a high temp.
If the worth of a gun does not justify a "Professional" re-hardening its usually best to leave as is.
A "Pseudo/Faux" (whatever you want to call it) coloring can be "Painted" on by warming the part to about 200°F & using cold blue. This will not in any way damage the existing hardness "Nor" will it look original. This method was recommended by Ithaca for their Perazzi made guns they formerly imported. These guns I believe had a heat-treated frame of alloy steel which was not suitable for traditional case hardening. This was apparently the way they were colored at the factory.
Under "No Circumstances" should a gun frame be "Spot Colored" by applying the tip of an acetylene torch to it as this simply makes a "Smorgasbord" of the existing hardness with soft spots intermingled with hard spots.
