We investigate flow structures in rotating Rayleigh-Bénard convection experiments in water using thermal measurements. We focus on correlations between time series measurements of temperature in the top and bottom boundaries. Distinct anticorrelations are observed for rapidly rotating convection, which are argued to attest to heat transport by convective Taylor columns. In support of this argument, these quasigeostrophic flow structures are directly observed in flow visualizations, and their thermal signature is qualitatively reproduced by a simple model of heat transport by columnar flow. Weakly rotating and nonrotating convection produces positively correlated temperature changes across the layer, indicative of heat transport by large-scale circulation. We separate these regimes using a transition parameter that depends on the Rayleigh and Ekman numbers, RaE3/2.