The utilization of shape design to improve heat transfer characteristics in heat convection fields is an important subject in engineering. This review paper explains a numerical solution for the shape design problems involving steady and unsteady heat convection fields. Reshaping for the shape design is carried out by traction method, which is proposed as an approach to solving shape optimization problems. The traction method is a shape optimization method with some advantages such as deformation analysis of pseudo-elastic bodies can be used in the shape update analysis and smoothness in shape update can be maintained. In steady-state heat convection fields, shape design problems that control the temperature distribution in the sub-domains of the heat convection field are introduced. The square integration error between the actual temperature distribution and the target temperature distribution in the specified sub-domains is employed as the objective functional for the shape design. In unsteady heat convection fields, two shape design problems are shown; these problems also involve control of the temperature distribution in sub-domains of the field. In the first problem, in a manner similar to the steady-state problem, the square integration error of the sub-domains during the specified period of time is used as the objective functional. In the second problem, a multi-objective shape design problem that utilizes a normalized objective functional is formulated for the problem to prescribe the temperature distribution and the total dissipated energy minimization problem. The shape gradient of these shape design problems for steady and unsteady fields is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Numerical analysis programs for shape design problems using the traction method are developed, and the validity of the demonstrated method is confirmed by results of 2D numerical analyses.