This paper presents an experimental analysis for minimizing the thermal contact resistance (R) between an optical fiber and copper heat sink by using the low-melting temperature alloy (LMTA) as the thermal interface material (TIM) subject to high-flux operation (up to 250 W ⋅ m−1). For the cases without LMTA, the temperature rise (ΔT) can easily surpass 195 °C at a heating load of 25 W ⋅ m−1. By contrast, ΔT is dramatically reduced to be less than 1 °C with LMTA as TIM with a much higher heating power of 150 W ⋅ m−1. The corresponding thermal resistance (R) can be reduced from 6.5–8.2 K ⋅ m ⋅ W−1 to 0.004–0.013 K ⋅ m ⋅ W−1. The improvement is far superior to existing studies. Besides, decreasing the surface roughness and increasing contact pressure also help to reduce R, especially for the cases when the LMTA is not melted. As the LMTA melts, a significant reduction of R by 56% is achieved as compared to the case without melting. The effect of surface roughness and contact pressure on the thermal contact resistance is also examined, and it is found that the influences are small once LMTA melts.