Calculation of the Casimir force between similar and dissimilar metal plates at finite temperature

The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite-temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T = 300 K and T = 350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.