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The damages and destructions on materials at the attachment point of an lightning arc are mainly caused by thermal effects. Pressure effects and shock waves which occur due to the high temperatures are mostly the consequence of these thermal processes. The calculation and prediction of the heating processes lead to a better understanding of the damage mechanisms. This allows the assessment and the design of materials and lightning protection components. The paper presents calculations for different materials and a critical comparison with some laboratory measurements. Investigated materials are several metals (Cu, Al, steel) on the one hand and carbon fibre composite (CFC) on the other hand. These materials differ in their electrical and thermal material parameters and in their reactions to the lightning arc stress. It was the aim of the calculations to determine the development of temperature distribution up to critical temperatures.