Thermal metamaterials, designed by transformation thermodynamics are artificial structures that can actively control heat flux at a continuum scale. However, fabrication of them is very challenging because it requires a continuous change of thermal properties in materials, for one specific function. Herein, we introduce tunable thermal metamaterials that use the assembly of unit-cell thermal shifters for a remarkable enhancement in multifunctionality as well as manufacturability. Similar to the digitization of a two-dimensional image, designed thermal metamaterials by transformation thermodynamics are disassembled as unit-cells thermal shifters in tiny areas, representing discretized heat flux lines in local spots. The programmed-reassembly of thermal shifters inspired by LEGO enable the four significant functions of thermal metamaterials—shield, concentrator, diffuser, and rotator—in both simulation and experimental verification using finite element method and fabricated structures made from copper and PDMS. This work paves the way for overcoming the structural and functional limitations of thermal metamaterials.