The behaviour of intermittent turbulent temperature fluxes is characterized in terms of a flux interval, defined as the time interval over which flux values are computed, and a flux threshold value. Fluxes whose magnitudes exceed the threshold value are defined as flux events while the times when the threshold is not exceeded are defined as gaps. Turbulent temperature flux data from five sites in Kansas, Utah, and Washington State, U.S.A. are examined within this descriptive framework. The turbulent event fraction fturb, the ratio of the time occupied by turbulent events to the total sampling time, is found to depend linearly on the average flux for the sampling period over a range of flux intervals, threshold values, and sampling times. As the average flux for a sampling period decreases toward zero, the median magnitude of the fluxes during the gaps also decreases but the median fluxes during the turbulent events become nearly independent of the sampling period average. A wide range of values of fturb is found for gradient Richardson numbers less than 0.3, indicating the possibility of considerable intermittency under weakly to moderately stable conditions