Heat transfer measurements and horizontally averaged temperature profiles for turbulent thermal convection with uniform volumetric energy sources are used to deduce the mean eddy heat flux in fluid layers bounded by two rigid isothermal planes of equal temperature. For Rayleigh numbers from 22 to 675 times the critical value based on linear stability theory, a positive and negative component of eddy flux are found. The positive component dominates the negative component and is found to occupy the upper 60% of the layer. The eddy flux results in conjunction with mean temperature profiles also permit estimates of the production of thermal variance across the layer.