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GIL technology provides beside high reliability the opportunity of transmitting high amounts of energy. Thermal calculations need to be carried out to fulfill the requirements of each individual installation concerning current load, ambient temperature and solar radiation. Analytical formulae exist for the first generation of GIL, similar to cable systems. For the second generation of GIL a CIGRE WG developed numerical methods for thermal calculations. To ease these calculations models based on thermal networks have been developed. Thus extensive thermal FEM calculations can be avoided.