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The presence of polymer transfer residues on graphene surfaces is a major bottleneck to overcome for the commercial and industrial viability of devices incorporating graphene layers. In particular, how clean the surface must be to recover high (>2500 W/mK) thermal conductivity and maximize the heat spreading capability of graphene for thermal management applications remains unclear. Here, we present the first systematic study of the impact of different levels of polymer residues on the in-plane thermal conductivity (κ r ) of single-layer graphene (SLG) fabricated by chemical vapor deposition (CVD). Control over the quantity of surface residue was achieved by varying the length of time each sample was rinsed in toluene to remove the poly(methyl methacrylate) (PMMA) support layer. The level of residue contamination was assessed using atomic force microscopy (AFM) and optical characterization. The thermal conductivity of the suspended SLG was measured using an optothermal Raman technique. We observed that the presence of polymer surface residue has a significant impact on the thermal properties of SLG, with the most heavily contaminated sample exhibiting a κ r as low as (905 +155/-100) W/mK. Even without complete eradication of surface residues, a thermal conductivity as high as (3100 +1400/-900) W/mK was recovered, where the separation between adjacent clusters was sufficiently large (>700 nm). The proportion of the SLG surface covered by residues and the mean separation distance between clusters were found to be key factors in determining the level of κ r suppression. This work has important implications for future large-scale graphene fabrication and transfer, particularly where graphene is to be used as a heat spreading layer in devices. The possibility of new opportunities for manipulation of the thermal properties of SLG via PMMA nanopatterning is also raised.