Significant research has been dedicated to the exploration of high thermal conductivity polymer composite materials with conductive filler particles for use in heat transfer applications. However, poor particle dispersibility and interfacial phonon scattering have limited the effective composite thermal conductivity. Three-dimensional foams with high ligament thermal conductivity offer a potential solution to the two aforementioned problems but are traditionally fabricated through expensive and/or complex manufacturing methods. Here, laser induced graphene foams, fabricated through a simple and cost effective laser ablation method, are infiltrated with poly(3-hexylthiophene) in a step-wise fashion to demonstrate the impact of polymer on the thermal conductivity of the composite system. Surprisingly, the addition of polymer results in a drastic (250%) improvement in material thermal conductivity, enhancing the graphene foam's thermal conductivity from 0.68 W/m-K to 1.72 W/m-K for the fully infiltrated composite material. Graphene foam density measurements and theoretical models are utilized to estimate the effective ribbon thermal conductivity as a function of polymer filling. Here, it is proposed that the polymer solution acts as a binding material, which draws graphene ligaments together through elastocapillary coalescence and bonds these ligaments upon drying, resulting in greatly reduced contact resistance within the foam and an effective thermal conductivity improvement greater than what would be expected from the addition of polymer alone. Published by AIP Publishing. [http://dx