In this thesis, the stationary thermal analysis of a heating induction operation was studied. This was a coupled electromagnetic - thermal nonlinear and transient induction coil act as a heat source, which has been investigated through a finite element method. A vertical hollow cylinder with a stationary coil on the cylinder was heated at a certain time. Impact of natural convection with air around the cylinders on both inner and outer cylindrical surfaces was considered. Also, impact of external radiation levels was measured in the intended environment. Then, the process was investigated for a solid cylindrical billet and cones. In this process, first magnetic field has been simulated by solving the Maxwell equations, and the constant heat source was obtained after solving these equations. Then the energy equation inside solid (energy conduction equation) was solved to obtain the temperature distribution in the cylinder caused by the constant heat source, taking into account the heat transfer boundary, at different times using the finite components. In other words, the temperature distribution within the cylinder at any time will be achieved by solving the coupled equations of conduction equation in solid body, natural convection equations with surrounding air and the equations of radiation from the outer surface of a cylindrical drum. In this case the cylinder material properties were temperature -dependent and with thermal changes at different times, these properties were changed and re-calculated. Thus, solving the problem requires solving three coupled equations including: electromagnetic equations, thermal conductivity and natural convection. The obtained results from this study shows that the outer temperature of solid body against induction heating in 7 seconds changes from 200 celsius up to 900 celsius. This escalation is dependent to inductor frequency and thickness of the solid body. Enlargement of the solid body thickness was resulted to decrease maximum temperature outer of surface that was exposed to induction heating. Increase in frequency has been caused to increase in temperature growth rate and development of maximum temperature. The temperature of those points of solid body that were not exposed to the induction heating, were increased in a lower rate. At the end it has a significant difference with those points that were exposed to the electro-magnetic induction. The radius difference of temperature distribution in thickness of solid body was low because of thinness of the standard pipe and higher rate of conductivity coefficient with extension of solution time this difference approaches to be zero. Eventually, the accuracy of results was obtained by comparing the results of the analytical solution using the Green's function for a stationary location phase in isolated boundary. Key words : Heat Transferring, Stati onary Inductive Heating, Numerical Solution