For the fabrication of core-shell structure bimetallic lead-free solder balls, both the critical temperature ($T_{cr}$) for the phase separation of two immiscible liquid phases and the temperature coefficient of the interfacial tension between the two separated liquid phases are required. In order to obtain this information, the temperature dependence of the surface tension of 60%Bi-24%Cu-16%Sn(-REM) alloys was measured using the constrained drop method. The slope of the temperature dependence of the surface tension changed clearly at a critical temperature for the separation of two immiscible liquid phases. The critical temperature of the 60%Bi-24%Cu-16%Sn alloy was estimated to be 1097K. An addition of 0.05% Ce decreased the critical temperature to 1085K, whereas that of 0.05% La increased it to 1117K. It was found that the surface tension and its temperature coefficient of the 60%Bi-24%Cu-16%Sn alloy were slightly increased by the addition of 0.05% Ce and 0.05% La. In addition, additions of Ce and La increased the temperature coefficient of the interfacial tension.