The purpose of this work is to carry a discussion on the use of temperature constraints in topological derivative-based heat sink design, presenting simple benchmark problems. The forward problem is governed by the steady-state heat conduction equation. The point-wise inequality constraint on the temperature is formulated with a quadratic penalty functional and its first-order topological asymptotic expansion is derived. We consider a two-phase domain with different thermal conductivity properties subjected to an uniform heat source. We are interested in obtaining the optimal material distribution which minimizes the volume of the better thermal conductive phase while satisfying temperature constraints and with a thermal compliance regularization term. The topology optimization problem is addressed with an efficient algorithm based on the topological derivative method, combined with a level set representation of the design domain. Numerical experiments have confirmed the expected trade-off between the optimal domain's volume and the temperature constraint, revealing the need of allocating more conductive material as tighter constraints are imposed. This type of constraint can also be used to impose connectivity constraints for manufacturing process, which is a current and relevant application of the present study.