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Graphene was recently proposed as a material for heat removal owing to its extremely high thermal conductivity. We simulated heat propagation in silicon-on-insulator (SOI) circuits with and without graphene lateral heat spreaders. Numerical solutions of the heat-propagation equations were obtained using the finite-element method. The analysis was focused on the prototype SOI circuits with the metal-oxide-semiconductor field-effect transistors. It was found that the incorporation of graphene or few-layer graphene (FLG) layers with proper heat sinks can substantially lower the temperature of the localized hot spots. The maximum temperature in the transistor channels was studied as function of graphene's thermal conductivity and the thickness of FLG. The developed model and obtained results are important for the design of graphene heat spreaders and interconnects.