The restoration of worn-out parts by electric-arc surface welding using a flux-cored wire with an aluminothermic filler is investigated. The study focuses on a plate made of Hadfield steel (110G13L), a material known for its challenging weldability. The welding process involves depositing three layers onto a preconditioned surface. The surface welding process is mathematically described based on the Prandtl–Reuss model incorporating the Duhamel–Neumann law in place of Hooke’s law and a modified von Mises yield criterion to account for the viscous properties of materials during irreversible deformation. The elastic moduli and yield stress are assumed temperature-dependent. Laboratory studies were conducted to determine the combined thermal effect on the welding process. It is concluded that applying the combined thermal effect during surfacing with flux-cored wire with aluminothermic filler reduces the intensity of residual stresses, thereby enhancing the performance and durability of the welded part.