Precision thermometry of the skin can, together with other measurements, provide clinically relevant information about cardiovascular health, cognitive state, malignancy and many other important aspects of human physiology. Here, we introduce an ultrathin, compliant skin-like sensor/actuator technology that can pliably laminate onto the epidermis to provide continuous, accurate thermal characterizations that are unavailable with other methods. Examples include non-invasive spatial mapping of skin temperature with millikelvin precision, and simultaneous quantitative assessment of tissue thermal conductivity. Such devices can also be implemented in ways that reveal the time-dynamic influence of blood flow and perfusion on these properties. Experimental and theoretical studies establish the underlying principles of operation, and define engineering guidelines for device design. Evaluation of subtle variations in skin temperature associated with mental activity, physical stimulation and vasoconstriction/dilation along with accurate determination of skin hydration through measurements of thermal conductivity represent some important operational examples.