The inclusion of convective heat transport in thermal metamaterials is not only necessary but also crucially important to expand our scope and capability in controlling heat at will. Ideally, a thermal metamaterial should be able to simultaneously and independently manipulate both the conductive and convective heat flows. However, such thermal metamaterials have not yet been realized so far. Here, we report on experimental realization of such thermal metamaterials, which are achieved via a design of liquid–solid hybrid thermal metamaterials to support thermal convection and conduction as well as their transformations with a topology transition. These findings may promote the regulation of local hot/cold spots in living cells or biological tissues without disturbing the human body’s environment.