Controlling thermal waves, transient temperature fluctuations propagating through materials, is crucial for thermal management in aerospace, mechanical engineering, and electrical systems with pulsed heat sources and periodic temperature variations. However, their rapid attenuation due to thermal relaxation makes precise control inherently difficult, and even more so in metadevices designed to perform complex functions. Existing effective medium theory, proposed for steady-state heat transfer, is limited in addressing the transient nature of thermal-wave propagation. Here, we propose a diffusive pseudoconformal mapping theory for thermal waves to design metadevices with isotropic materials. As a specific application, we simultaneously design thermal-wave insulating and zero-index carpet cloaks within a unified spatial transformation framework. Furthermore, we uncover a geometric duality between these functionally distinct devices. Numerical simulations show that these cloaks with a carpetlike surface achieve precise invisibility in thermal-wave environments. Meanwhile, objects covered by the zero-index cloak can also sense background temperature variations, similar to sensors detecting environmental changes. We further integrate common materials with a segmented outer-layer structure and propose an experimental scheme to validate the feasibility of cloaks. Our research builds a broader pseudoconformal framework and advances the design of thermal-wave metadevices.

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• Cloaking
• Heat transfer
• Thermal conductivity
• Metamaterials
• Optical conformal mapping
• Thermal techniques
• Transformation optics