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A rigorous analytical analysis of DC SQUIDs having reduced inductance smaller than 1//spl pi/ and operating in the presence of thermal fluctuations has been developed. On the basis of the Fokker-Planck equation the expressions for the output voltage across the Josephson junctions and the circulating current in the SQUID loop were found. This reduces the problem of finding all important SQUID characteristics (current-voltage curves, dynamic resistance, transfer function, and energy sensitivity) and their optimization to a simple exercise of elementary mathematics. As expected, the present analytical approach gives unique insights and significantly contributes to understand the physics related to the effects of large thermal fluctuations on system's operation.