A thermal cloak can hide an object inside the cloak from the detection by measuring external heat flow (outside the cloak); this behavior is called the cloaking effect. However, such a thermal cloak has a limitation. Namely, the object is always located inside the cloak's central region with a homogeneous temperature distribution, and hence this object cannot feel the flow of heat. To overcome the limitation, we develop a coordinate transformation method to design a complementary material, and add it into the central region of the cloak. As a result of finite element simulations, in case of external heat flow, the temperature distribution in this central region becomes inhomogeneous and hence the object feels the flow of heat indeed. Meanwhile, the cloaking effect remains the same, or almost the same as the cloak without such a complementary material inside. Thus, it becomes possible to use complementary materials to design thermal devices where heat conduction can be controlled at will. (C) 2014 Elsevier Ltd. All rights reserved.