Vacuum glazing consists of two glass sheets with a narrow internal evacuated space. The separation of the sheets under the influence of atmospheric pressure is maintained by an array of small support pillars. The thermal resistances associated with the heat flow through individual pillars, and through the pillar array, are calculated using a simple analytic method, and by more complex finite element models. The results of both approaches are in very good agreement, and are validated by comparison with experimental data. It is shown that, for many purposes, the amount of heat which flows through the pillars can be determined without incurring significant errors by assuming that the heat flow is uniformly distributed over the area of the glass. Finite element modelling, and a superposition method, are used to determine the temperature distribution on the external surfaces of the glass sheets due to pillar conduction. Again the results obtained with both approaches are in very good agreement. An approximate method is described for calculating the magnitude of these temperature non- uniformities for all practical glazing parameters.