All the thermal cloaks reported in the literature can be used to hide an object inside the cloak. However, a common limitation of this kind of thermal cloaks is that the cloaked object cannot feel the external heat flow; thus we call these cloaks "conventional thermal cloaks". Here we manage to overcome this limitation by exploiting a class of unconventional thermal cloaks. Our finite element simulations show the desired cloaking effect. The underlying mechanism originates from the complementary effect of thermal metamaterials. This work suggests a different method to design thermal devices.