The imaging of the distribution of thermal conductivity tensor at various points in a tissue is an essential need when accurate knowledge of heat energy flow in tissue is required for diagnostic and therapeutic management in oncology, neurology, and interventional radiology. Conventionally, tissue thermal conductivity is assumed as scalar, which induces errors in obtaining proper heat flow distribution. Using statistical thermodynamics principles, we present a method for constructing thermal conductivity tensor image of a tissue or an organ, using an MRI scanner. We elucidate the necessary tensorial cross-property relationship between different transport processes and confirm the same by experimental data. Using the proposed method, we perform a preliminary study of the procedure of thermal conductivity tensor imaging of the human brain as a case study. The methodology is quantitatively elucidated by measurement of tissue anisotropy distribution, tensor eigenvalues, and path tracking, along with three illustrative examples showing that transport properties estimated by the proposed thermal conductivity approach closely corroborates, with over 90% accuracy, to the experimentally measured values of the transport parameters which have been independently experimentally measured directly. By combining diffusion and perfusion tensor imaging approaches using mobility-encoding and spin-labelling methodologies respectively, we delineate the possible applications of this novel imaging modality to clinical problems of energy flow mapping involving biological heat transfer equations, such as planning of hyperthermic treatment to brain tumors, and electrode localization for deep brain stimulation in Parkinson's disease.