  Remote temperature control can be obtained by a long-focus thermal lens that
can focus heat fluxes into a spot far away from the back surface of the lens
and create a virtual thermal source/sink in the background material, around
which the temperature field distribution can be remotely controlled by changing
the parameters of the thermal lens. However, due to the lack of negative
thermal conductivity, the existing thermal lenses have extremely short focal
lengths and cannot be used to remotely control the temperature field around the
virtual thermal source/sink. In this study, we theoretically propose a general
approach to equivalently realize negative thermal conductivity by elaborately
distributed active thermal metasurface (ATMS), then use the proposed ATMS to
implement a novel thermal lens with long focal length designed by
transformation thermodynamics, and experimentally verify the performance of the
designed long-focus thermal lens with measured focal length f=19.8mm for remote
heating/cooling. The proposed method expands the scope of the thermal
conductivity and open up new ways to realize unprecedented thermal effects with
effective negative thermal conductivity, such as "thermal surface plasmon
polaritons", thermal superlens, thermal tunneling effect, and thermal invisible
gateway.
