This paper treats the Joule heat welding of thin Pt wires having various diameters. Joining of fine-scale materials, such as micro-or nanowires, has been essential to create advanced materials systems. Joule heat welding is one of the suitable way for this purpose. It has been reported that thin wires were welded together under the supply of constant direct current, and the welding condition was sensitive to the thermal boundary conditions around the wires under the current supply, which was affected by the heat transfer from the wire surface to the ambient and the heat conduction at the ends for the current supply. The diameters of thin Pt wires were 0.8-20 m, and the current required to cut the wire by Joule heating was investigated. The temperature of the wire having the smaller diameter was easily increased by Joule heating, and this became remarkable with increasing the slenderness ratio, i.e., the ratio of the diameter to the length for current supply. An index related to the temperature of the wire under the current supply was introduced to describe the thermal boundary conditions around the wire. The behavior of the index against the diameter was approximated by the exponential functions, and the thermal boundary conditions around the wires having various diameters became predictable. Finally, the validity of the thermal boundary conditions determined and predicted in this study was verified by conducting the experiments to cut and weld the wires by Joule heating.