The tundish with heating instrumentation is attracting more and more attention in continuous casting processes for maintaining a pre-determined constant pouring temperature under a given casting speed, which is beneficial for an improved and consistent steel product quality. However, the fluid flow, temperature distribution and the removal behaviors of non-metallic inclusions in it will be much different from that in a conventional tundish, due to the implementation of the heating practice. In the present work, to reduce the non-metallic inclusion amounts in billets of the second and sixth strands in a seven-strand tundish with channel type induction heating, the flow field profiles and temperature profiles of molten steel in this tundish have been investigated using hydrodynamic modeling coupled with mathematical simulation under isothermal and non-isothermal situations, respectively. The results of the isothermal experiment indicate that the prototype tundish has severe “short-circuiting flow” in the second and sixth strands, which might have caused the increased inclusion amounts in the billets of the two strands. The flow field of the tundish can be greatly improved by changing the channel design and adding two high dams at each side of the tundish. Compared with the prototype structure A0, the average residence time of the optimized case C5 is prolonged by 55.49% (from 501 to 779 s); the dead zone volume fraction is reduced by 66.18% (from 45.57% to 15.41%); and the flow of each strand becomes more consistent with lower standard deviation. The non-isothermal experiments show that the fluid presents an obvious rising tendency when it flows out from the heating induction channel. The larger the temperature difference inside and outside the channel is, the more consistent the fluid flow between different strands and the more homogeneous the flow field in the whole tundish. For the prototype tundish structure, when the temperature difference is 5 °C, the dead zone is basically eliminated, and the minimum residence time is prolonged by 789% (from 38 to 338 s), compared with the 0 °C of temperature difference. A mathematic model has been proposed accordingly, which can explain well the hydraulic phenomena. The inclusion removal rates of different cases were compared by mathematical simulation, and their removal mechanism was studied, as well.