With the wide deployment of electrical heating devices

such as electric boilers and heat pumps

the coupling between electric power and heating system is increasingly prominent. Under the circumstance that multiple energies taking part in the trading market

sophisticated games exist between various market participants. Analyzing consumers' behaviors and their impacts on the energy prices becomes an important issue. A heat-power trading scheme is proposed and the optimal decision making problem of consumer with constant elasticity of substitution(CES)utility function is formulated. The proposed method also provides important reference for the research on other energy market problems. The market clearing condition is transformed into mixed integer linear constraints by jointly using the Karush-Kuhn-Tucker(KKT)optimality condition as well as the duality theorem of linear programming. Embedded with the market clearing condition

the consumer decision making problem is solved by the pattern search algorithm. Numeric studies on a testing system consisting of an IEEE 33 bus distribution system and a 32 node heating system show the effectiveness of the proposed method. The influences of several factors on the market equilibrium are also analyzed.