The paper presents a formulation for support optimization to maximize heat dissipation in additive manufacturing. To simulate heat transfer from the part to the supports, a boundary-dependent heat flux is applied on the part/support interface. Since the density-based topology optimization does not involve explicit boundary, the heat flux is implicitly imposed through a domain integration of a Heaviside projected density gradient. As such, this formulation also supports simultaneous optimization of support and parts in additive manufacturing. Self-supporting supports are obtained by controlling the anisotropic thermal conductivity of the supports. Three different objective functions related to heat dissipation efficiency are investigated. Numerical examples are presented to demonstrate the validity and efficiency of the proposed approach.