Researchers aim to produce sustainable insulation materials using lignocellulose fibres (natural plant fibres). Lignocellulose fibres are readily available, biodegradable, and low-cost materials for insulation. However, these materials are formulated as composites and not as fibres alone. Thus, the thermal properties of these composites depend on the volume fraction of each phase. The evaluation of thermal conductivity can be followed by experimental, analytical, and numerical methods. Numerical and analytical methods are convenient investigational methods; they are more cost-effective, have a higher degree of flexibility in design enhancement, and are faster methods of analysing results than the experimental method. The thermal conductivity value of each phase should be used to analyse the thermal properties of composite materials. However, there is no specific method to determine the thermal conductivity of natural fibres. Therefore, this work suggests a new method to find the thermal conductivity of coir fibres. The method follows the inverse calculation of the analytical methods to find the thermal conductivity of coir fibres, and the substitution values for the equations will be determined by an experimental method. The two-phase composite was fabricated by coir fibres and epoxy with different volume fractions. Next, the thermal conductivity was measured for the fabricated composite and epoxy using the hot disk method. Finally, the transverse thermal conductivity of the fibre was calculated using available analytical models namely, the Rule of mixture, Maxwell's model, Rayleigh's model, and the Lewis-Nielsen model. The thermal conductivity value determined was 0.3058 W/mK. The results were validated through numerical modelling. The thermal conductivity of fibres was determined using a binderless compacted fibre disk, and the obtained value was 0.2797 W/mK. This value was correlated with the results obtained with the analytical and numerical methods.