A numerical model has been developed to study heat transfer in a silicon carbide crystal growth system. Both the electromagnetic field and temperature distribution are calculated and the effects of as-grown crystal length and coil current on temperature field are investigated. An order-of-magnitude analysis and one-dimensional network model are also employed to investigate the transport phenomena in the growth system. The results obtained from the network analysis compare well with the two-dimensional simulations. Thr interface temperature is found to increase with the ingot length, and a nonlinear relationship exists between the maximum temperature in the furnace and electric current.