The advent of high-temperature (i.e., metal-carbon eutectic) fixed points (HTFP) has placed high demands on the equipment needed to implement them. In particular, the HTFP performance is sensitive to the thermal environment. The temperature gradient in the crucible volume determines the duration and form of the melting plateau, and a gradient in the wrong direction along the crucible can result in mechanical damage. With an emphasis on crucibles for contact thermometry, a transient thermal model, which employs the finite element method is described. The aim is to optimize the HTFP environment, and to evaluate the relationship between the temperature of the liquid-solid interface (the actual fixed-point temperature) and the temperature measured by the contact thermometer (the measured fixed-point temperature). A simple mechanism to minimize temperature gradients along the HTFP cell axis is also presented. Importantly, the model shows that the actual temperature of the liquid-solid interface during melting is given by the indicated temperature at the end of the plateau, i.e., the liquidus point, not the point of inflection of the plateau, as is currently the convention. This does not significantly affect the conventional pure metal fixed points of the ITS-90, but could have ramifications for the new generation of high-temperature fixed points where the melt takes place over a temperature range and the liquidus temperature has yet to be identified.
