We quantify the transport of sea surface temperature (SST) from SST fluctuations. Previous studies have estimated the advective transport of SST from time-lag correlation of SST anomalies. However, this approach does not consider diffusive SST transport or relaxation to atmospheric temperatures. To quantify the transport more completely we use a response function (Green's function) which solves the SST continuity equation for an impulsive forcing. The response function is estimated from SST anomalies using a fluctuation-dissipation approach. Decomposing the linear operator into symmetric, anti-symmetric, and divergent operators enables estimates of the model's spatially dependent velocity vector, diffusivity tensor, and relaxation rate.