High-repetition-rate, two-point Rayleigh thermometry is used to measure the thermal dissipation in turbulent nonpremixed jet flames. Scalar-dissipation measurements are very important in turbulent combustion but are often strongly influenced by noise effects. Dissipation is proportional to the squared gradient of the scalar, and noise produces an "apparent dissipation" that can dominate the measured dissipation, particularly at high resolution. Two independent techniques are presented that enable correction for the apparent thermal dissipation, provided that the smallest spatial scales are resolved. A model for shot-noise-limited data is developed that predicts the magnitude of the apparent dissipation at any measurement location and gives the minimum value of the apparent dissipation for measurements that are not shot-noise limited. These techniques are applied to the Rayleigh thermometry data, and they are shown to be largely self-consistent and consistent with theoretical expectations. The apparent dissipation is significantly larger than the true dissipation, demonstrating the importance of data correction in this noise-limited, fully spatially resolved regime.