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Multipole wigglers in storage rings already produce X-ray power in the range up to a few kilowatts and planned devices at third-generation facilities promise up to 30 kW. Although the power density at the monochromator position is an order of magnitude lower than that from undulators, the thermal strain field in the beam footprint can still cause severe loss of performance in X-ray optical systems. For an optimized adaptive design, the results of finite-element analysis are compared with double-crystal rocking curves obtained with a laboratory X-ray source and, in a second paper [Quintana, Hart, Bilderback, Henderson, Richter, Setterson, White, Hausermann, Krumrey & Schulte-Schrepping (1995). J. Synchotron Rad. 2, 1-5], successful tests at wiggler sources at CHESS and ESRF and in an undulator source at HASYLAB are reported.