Dear Tim:
You have to make a clear differentiation between plastic deformation (given at micro scale) and what you call "deformation" that I have taken as distortion (at macro scale). The former, is given near the welded joints where the residual stresses are high enough and you surpass the yield strenght by mechanical or, as you said, thermal energy (wich is the case of the thermal stress relief); this plastic deformation allows the stress relief around the welded joint. For other side, distortion is caused by the loss of strength of the weldment (or vessel in your case) if it is not properly supported or if its own stiffness at the temperature of the heat treatment is not enough to support its own weight (for example, thin walled large diameter vessels without internal stiffening is a case very susceptible to distortion during a heat treatment).
Then, you do not gonna find a only method for predict distortion during the heat treatment (wich does not mean that does not exist methods) because each particular geometrie of weldment is different to others and, then, its susceptibility to distortion is different too.
You may analize your particular case and design a proper support and, if it is necessary, temporary stiffening in order to avoid distortion during the heat treatment and keep the dimensional stability of your weldment. Other mechanical methods, as vibratory or overload, have no this trouble but your efficacy in stress relief, for what I know, is not so good as thermal treatments.

I hope this help you.

Dear Tim:

You have to make a clear differentiation between plastic deformation (given at micro scale) and what you call "deformation" that I have taken as distortion (at macro scale). The former, is given near the welded joints where the residual stresses are high enough and you surpass the yield strenght by mechanical or, as you said, thermal energy (wich is the case of the thermal stress relief); this plastic deformation allows the stress relief around the welded joint. For other side, distortion is caused by the loss of strength of the weldment (or vessel in your case) if it is not properly supported or if its own stiffness at the temperature of the heat treatment is not enough to support its own weight (for example, thin walled large diameter vessels without internal stiffening is a case very susceptible to distortion during a heat treatment).

Then, you do not gonna find a only method for predict distortion during the heat treatment (wich does not mean that does not exist methods) because each particular geometrie of weldment is different to others and, then, its susceptibility to distortion is different too.
You may analize your particular case and design a proper support and, if it is necessary, temporary stiffening in order to avoid distortion during the heat treatment and keep the dimensional stability of your weldment. Other mechanical methods, as vibratory or overload, have no this trouble but your efficacy in stress relief, for what I know, is not so good as thermal treatments.

I hope this help you.

Jorge Giraldo
Medellín, Colombia