Below the freezing point of silver, radiation thermometers are generally calibrated by implementing the multi-point interpolation method using blackbody measurements at three or more calibration points, rather than the ITS-90 extrapolation technique. The interpolation method eliminates the need to measure the spectral responsivity and provides greater accuracy at the longer wavelengths required below the silver point. This article identifies all the sources of uncertainty associated with the interpolation method, in particular, those related to the reference blackbody temperatures (either variable-temperature or fixed-point blackbodies) and to the measured thermometer signals at these points. Estimates are given of the ‘normal’ and ‘best’ uncertainties currently achievable. A model of the thermometer response is used to propagate all the uncertainties at the reference points and provide a total uncertainty at any temperature within the calibration range. The multi-point method has the effect of constraining the total uncertainty over this range, unlike the ITS-90 technique for which the uncertainties propagate as T2. This article is a joint effort of the working group on radiation thermometry of the Consultative Committee for Thermometry (CCT), summarizing the knowledge and experience of all experts in this field.