The heat transfer and liquid phase convection during GaInSb crystal growth via the traveling heater method (with a seed) were investigated using numerical simulation to optimize the process parameters and shorten the experimental period in order to produce a high-quality crystal widely used to make various optoelectronic devices. There will be a phenomenon of “thermal impermeability” with an increase in crystal radii for the same furnace temperature profile. The maximum furnace temperature should display an increase of at least 1030 K to 1060 K in order to ensure the successful introduction of the seed with an increase of the crystal radius from 0.01 m to 0.03 m. The interface bending of the solid–liquid interface significantly increases with an increase of the crystal radius from 0.01 m to 0.02 m by about 50%, 67%, and 140%, corresponding to the maximum furnace temperatures 1030 K, 1040 K, and 1050 K, respectively. However, it decreases significantly when the maximum temperature increases from 1030 K to 1050 K, from 0.16 to 0.05, 0.2 to 0.105, and 0.24 to 0.12, corresponding to the crystal radii 0.01 m, 0.015 m, and 0.02 m, respectively. The maximum flow velocity of melt increases slightly with the furnace maximum temperature for the same radius, less than about 6%. However, it increases significantly with the increase of the radius from 0.01 m to 0.02 m, more than 68%.