For the purpose of finding a way to control effectively the residual thermal stresses induced by local heat treatment on spherical vessels, a thermal tracing program is developed successfully based on the transient thermal analysis and controlling method of average temperature of nodes located in an "observed region." Typical calculation cases reveal that the local heat treatment process itself does cause obvious residual thermal stress that is high enough to cause yield when concentrated heating on small region is adopted, but decentralized heating on a larger region can lower effectively the residual thermal stresses to a rather desirable level. It can be found through a one by one analysis of ten factors, which are possibly influential on residual thermal stress: arc radius of heated region, holding temperature, volume, and wall thickness of the vessel are primary effective factors. The bandwidth of the annular insulated region, the heating rate, and the size of the observed region are secondary factors. Heating pattern, holding time, and cooling rate can hardly affect the residual thermal stress. Considering the primary factors except holding temperature, and taking 30% of yield stress as the expected residual thermal stress level, the recommended arc radius of heated region should be 2.2 Rt in minimum.