Topology optimization of the heat transfer quality in two-dimensional heat conduction problem at enclosure as one of the typical thermo-physical problems has always been quite important. In this paper a level set-based topological optimization procedure of two-dimensional heat conduction problem include point and speared thermal on computational domain load using finite elements method is developed. In level-set method, all structural boundaries are parameterized by a level of dynamic implicit scalar function of higher order. Changes of this function can easily model the detachment and attachment of dynamic boundaries in topology procedures. The same shape functions of finite elements analysis are employed to approximate the unknown temperatures and geometry modeling of the design domain. The objective function is to minimize thermal power capacity and sensitivity analysis on some heat conduction problems is investigated to deal with the topology optimization using level-set method with the finite elements scheme. Finally, topology optimization results of 3 heat conduction problems under both include point and spread thermal load cases are presented to demonstrate the validity of the proposed method. The proposed method lead to a significant reduction of the computational cost and time and it can be applied to a wide range of topology optimization problems arising from the heat transfer.