The analysis is complicated by the circular nature of the problem: biases in SST depend on the heat fluxes, which are calculated from the SST. The analysis method uses pairs of co-located SST observations obtained by different measurement techniques: one ship using an insulated bucket to measure the SST and the other reporting the temperature of the engine intake water. A simple physically based model is used to parameterise the expected difference between the two observations based on environmental conditions. The simplest model parameterises the night-time heat loss from bucket-measured SST by the air-sea temperature difference and allows for a constant offset between the two reports. In order to estimate the empirical coefficients in the model it is necessary to account for the error structure of the dataset. Random errors for each variable in the model are calculated from the data, along with correlations between these errors. The effect of the errors and correlations are then removed, and the empirical coefficients derived. The results suggest that night-time bucket SST may be biased cold. The magnitude of the bias varies with the air-sea temperature difference, on average being 0.3°C. The mean offset between the bucket SST and engine intake SST is close to zero, once the cold bias in the bucket SST is accounted for. This contradicts previous studies which concluded that engine intake SST is, on average, biased warm due to heating of the water by the ships engines. There was no evidence for that conclusion. This bias in the bucket-derived SST observations of order a few tenths °C is climatologically significant; the magnitude of the effect will vary with time due to trends in the proportion of reports made by different observing methods.