The existing theoretical models of heating by concentrated sources with a high energy density generally describe processes with deep penetration welding of part surfaces. The purpose of this study is to identify the factors that have a major effect on hardening of parts through heat treatment with a high-speed or pulsed scanning stationary heat source, which creates a uniform temperature field. Using methods of regression analysis, the authors derived equations for calculating the hardening depth in the proposed hardening process, the rate and time of steel cooling in a critical temperature range. The paper presents the calculated parameters of the hardening process in which parts, including wheel flanges of locomotives, are heated by a plasma arc in nitrogen. The findings can be used to reduce costs of complex experiments aimed at selecting surface heat hardening parameters to increase the service life of locomotive mechanical parts.