The knowledge of the thermal conductivity of nuclear fuel and its evolution as a function of temperature and burn up is a major challenge in the context of the evaluation and understanding of irradiated fuel performances in current reactors. It is also the case for the development and qualification of fuel for future reactors. Indeed, numerical simulations of the fuel behaviour under various conditions require the accurate knowledge of thermal conductivity over a wide range of temperature (from ambient to melting point temperature) but also at the scale of few tens of micrometres to take into account the microstructural effects on the thermomechanical evolution of the fuel in normal or incidental irradiation conditions. Different methods, using laser matter interactions, can deduce the thermal conductivity from a thermal diffusivity measurement. In this paper, the potential of two techniques, which present spatial resolution from millimetre to few tens microns, are discussed in the context of the determination of the fuel thermal conductivity: laser flash method and infrared microscopy. Experiments on graphite, as material model, have been conducted and validate these two thermal diffusivity measurement techniques. We present a measurement example for both methods on graphite and then a first experiment carried out with the infrared microscopy technique on UO$_2$ .