The evolution of both the core melting and fiber fuse phenomena in a single-mode fiber-optic connector was studied theoretically. Carbon black was chosen as a light-absorbent material. A thin absorbent layer with a thickness of 1 m order was assumed to be formed between the fiber end faces in the connector. When a high-power laser operating at 1.48 or 1.55 m was input into the connector, the temperature on the fiber core surface increased owing to heat conduction from the light-absorbent material. The heat flow process of the core, which caused the core to melt or the fiber fuse phenomenon, was theoretically calculated with the explicit finite-difference method. The results indicated that initial attenuation of less than 0.5 dB was desirable to prevent core fusion in the connectors when the input 1.48 m laser power was 1 W. It was found that a core temperature of more than 4000 K was necessary to generate and maintain a fiber fuse.