Extremely High Thermal Conductivity of Graphene: Experimental Study
  We report on the first measurement of the thermal conductivity of a suspended single layer graphene. The measurements were performed using a non-contact optical technique. The near room-temperature values of the thermal conductivity in the range ~ 4840 to 5300 W/mK were extracted for a single-layer graphene. The extremely high value of the thermal conductivity suggests that graphene can outperform carbon nanotubes in heat conduction. 
A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao   and C. N. Lau