Laminar pyrocarbons are used as interphases or matrices of carbon/carbon and ceramic-matrix composites in several high-temperature aerospace applications. Depending on their organization at the microscale, they can have a variety of mechanical and thermal properties. Hence, it is important to know, before thermal processing, the properties of these matrices at the micrometer scale in order to improve and control the composite behavior in a macroscopic scale. We use Scanning Thermal Microscopy (SThM) on a silica fiber / regenerative laminar pyrocarbon matrix composite to provide an insight into the effective thermal conductivity of pyrocarbon as well as the thermal contact resistance at the interface between fiber and matrix. The conductivity of pyrocarbon is discussed as a function of its nanostructural organization.