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An inverse method is presented for the estimation of geothermal reservoir initial temperatures based on a control theory algorithm in which computed well temperatures are fitted to well-logged temperatures. The method and results are presented in a two-part paper. Part I deals with the mathematical model of the well and the formation while Part II presents the inverse control algorithm and results of application. Well temperatures are obtained by simulating the circulation and shut-in processes in the presence of lost circulation using macroscopic balances to describe momentum and energy transport. Transport processes in the formation consider the reservoir as an isotropic porous medium with Darcian flow. Computed well temperatures are fed to the inverse control algorithm to estimate the initial formation temperatures. The method was applied to the estimation of the initial formation temperatures of well LV-3 from the Las Tres Virgenes, Mexico, geothermal field, as described in Part II of this paper. [ABSTRACT FROM AUTHOR]