Holding mixtures of solid and liquids at a high temperature is a common process in sterilising food material. It is difficult to measure the temperature of a particle flowing down the holding tube. Differences in velocity and temperature between different particles must however be estimated in order to allow prediction of process times. Experiments show that some particles may spend extended periods of time at or near the walls of the tube; the thermal behaviour of particles propagating along the wall may differ from those in the bulk. A mathematical model has considered this problem for the case of a rectangular shaped particle sliding on the pipe wall. Analytical solutions of the conduction equations are not available; a two-dimensional finite element program, using a novel dynamic moving mesh, has been developed to simulate the moving particle. Temperature differences between wall and bulk have been shown by the model.