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Thermal interface material (TIM) that exists in a liquid state at the service temperature enables efficient heat transfer across two adjacent surfaces in electronic applications. In this work, the thermal conductivities of different phase regions in the Ga-In system at various compositions and temperatures are measured for the first time. A modified comparative cut bar technique is used for the measurement of the thermal conductivities of GaxIn1−x (x = 0, 0.1, 0.214, 0.3, and 0.9) alloys at 40, 60, 80, and 100 °C, the temperatures commonly encountered in consumer electronics. The thermal conductivity of liquid and semi-liquid (liquid + β) Ga-In alloys are higher than most of the TIM’s currently used in consumer electronics. These measured quantities, along with the available experimental data from literature, served as input for the thermal conductivity parameter optimization using the CALPHAD (calculation of phase diagrams) method for pure elements, solution phase, and two-phase region. A set of self-consistent parameters for the description of the thermal conductivity of the Ga-In system is obtained. There is good agreement between the measured and calculated thermal conductivities for all of the phases. Due to their ease of manufacturing and high thermal conductivity, liquid/semi-liquid Ga-In alloys have significant potential for TIM in consumer electronics.