The search for technological options to obtain strong units with small deformation values determines the study of the local thermal effect on the distribution of residual stresses in permanent joints of metal structures made by arc welding with forced cooling. The mathematical model is based on the Prandtl-Reiss model in which the Hooke law is replaced by the Duhamel-Neumann law and the Mises criterion is supplemented by the Johnson-Cook strain hardening function. The elastic moduli, as well as the yield strength, are assumed to be temperature-dependent. The calculated values of residual stresses show the positive effect of forced cooling of the welded zone.