A cooling circuit for an internal combustion engine, including a circulation pump of a coolant, a control device able to temporarily maintain the cooling circuit in a non-active state following a start of the internal combustion engine and to thus temporarily prevent a circulation of the coolant in the cooling circuit by stoppage of the pump, characterized in that said control device includes: an iterative estimation module of temperatures, able to deliver during the temporary stopping of circulation of the coolant, on (N + 1) outlet paths on the one hand N estimated values of the respective temperatures of a plurality of thermal nodes each characterizing a temperature of a solid or liquid physical element of the engine concerned as sites of the engine essential for the monitoring of the thermal state of said engine and, on the other hand, a (N +1)th value which is an estimated value of the temperature of the coolant, N representing a whole number, this module including the implementation of a modelling of the thermal exchanges occurring between the N thermal nodes concerned in the engine, a presentation module of input data (21, 26), able to provide, during the temporary stoppage of circulation of the coolant, to the iterative estimation module of temperatures a first series of M input signals, respectively associated with M operating parameters of the engine, and a second series of (N + 1) input signals, constituted by the (N + 1) preceding available estimated values, present at the output of said iterative estimation module of temperatures, M representing a whole number, a comparison module, able to provide during the temporary stoppage of circulation of the coolant a difference signal between the estimated value of the temperature of the coolant and a measured value of said temperature, a first correction stage (24, 25), able to carry out during the temporary stoppage of circulation of the coolant, on the (N + 1) outlet paths of the iterative estimation module of temperatures a correction based on the difference signal resulting from said comparison, and a second correction stage (31, 32, 33, 34), able to carry out on the M input signals of the M input paths of the iterative estimation module of temperatures a second correction on the basis of the result of said comparison. an iterative estimation module of temperatures, able to deliver during the temporary stopping of circulation of the coolant, on (N + 1) outlet paths on the one hand N estimated values of the respective temperatures of a plurality of thermal nodes each characterizing a temperature of a solid or liquid physical element of the engine concerned as sites of the engine essential for the monitoring of the thermal state of said engine and, on the other hand, a (N +1)th value which is an estimated value of the temperature of the coolant, N representing a whole number, this module including the implementation of a modelling of the thermal exchanges occurring between the N thermal nodes concerned in the engine, a presentation module of input data (21, 26), able to provide, during the temporary stoppage of circulation of the coolant, to the iterative estimation module of temperatures a first series of M input signals, respectively associated with M operating parameters of the engine, and a second series of (N + 1) input signals, constituted by the (N + 1) preceding available estimated values, present at the output of said iterative estimation module of temperatures, M representing a whole number, a comparison module, able to provide during the temporary stoppage of circulation of the coolant a difference signal between the estimated value of the temperature of the coolant and a measured value of said temperature, a first correction stage (24, 25), able to carry out during the temporary stoppage of circulation of the coolant, on the (N + 1) outlet paths of the iterative estimation module of temperatures a correction based on the difference signal resulting from said comparison, and a second correction stage (31, 32, 33, 34), able to carry out on the M input signals of the M input paths of the iterative estimation module of temperatures a second correction on the basis of the result of said comparison.