Effective thermal design, pivotal for nanoelectronics development, relies on understanding the heterogeneous interfaces of nano-polymer composites. In particular, the contact mode between heterostructures significantly influences interfacial thermal conductance (ITC), a key factor in device performance optimization. Employing molecular dynamics simulations, this study systematically investigated the ITC of graphene and cellulose heterostructures, examining different contact modes-line contact and surface contact-and the influences from nanoscopic factors such as spacing, overlap distance, and functional groups. Our findings demonstrate that in the line contact mode, ITC increases with decreased spacing, primarily due to the enhanced phonon matching at low frequencies. Conversely, in the surface contact mode, ITC (MW/m2K) decreases while thermal conductance (TC, pW/K) increases with an increasing overlap distance (area), which also results in a sparser cellulose structure, as indicated by the radial distribution function. Functionalized graphene significantly boosts ITC in both modes by improving interfacial coupling and phonon matching, with hydrogen bonding intensifying this effect. Moreover, the study reveals that different contact modes lead to distinct heat transfer mechanisms. In line contact mode, inplane phonons play a dominant role, while in surface contact mode, out-of-plane low-frequency phonons is notably increased. These comprehensive insights deepen our understanding of the heat transfer across graphenepolymer interfaces with different contact modes, offering valuable guidance for designing highly thermally conductive composites for effective thermal management.