This scientific monograph discusses the numerical analysis of a PID controlled and temperature constrained welding process. Temperature controlled welding may be essential amongst others to prevent deformation, residual stress or for in-service gas pipeline maintenance. This book discusses a method to model such a controlled welding process through finite element analysis. The Goldak moving heat source model representing the arc welding process has been implemented into the proprietary macro language of ANSYS, APDL. Algorithms have been developed to take readings of temperature levels on the workpiece surface and adjust the welding thermal output accordingly. Several tests have been carried out to verify the functionality of this model. In addition to the comparison of required versus achieved temperature profiles, the control error and the controller output is assessed in this monograph. The results are compared with a simplified mathematical model and basic control quality indicators are calculated. As it follows from the conclusions, the results obtained by the simulations are realistic and the controller follows the prescribed temperature profiles within reasonable accuracy.