Provided are tissue-mounted devices and methods for monitoring a thermal transport property (e.g., thermal conductivity, thermal diffusivity, heat capacity) of tissue, such as skin. The devices conformally mount to the tissue and have one or more thermal actuators and a plurality of sensors. The actuator applies heat to the tissue and the sensors to detect a spatio temporal distribution of a physiological tissue parameter or physical property resulting from the heating. This spatio temporal information may be correlated with a rate, velocity and/or direction of blood flow, the presence of a vascular occlusion, circulation changes due to inflammation, hydration level and other physiological parameters.