A modern gas turbine engine (GTE) is a complex nonlinear dynamic system with the mutual effect of gas-dynamic and thermal processes in its components. The engine development requires the precise real-time simulation of all main operating modes. One of the most complex operating modes for modeling is “cold stabilization,” which is the rotors acceleration without completely heated up the turbine elements. The dynamic heating problem is a topical practical issue. Solving the problem requires coordinating a gas-path model with heat and stress models, which is also a significant scientific problem. The phenomenon of interest is the radial clearances change during engines operation and its influence on engines static and dynamic performances. To consider the clearance change, it is necessary to synthesize the quick proceeding stress-state models (QPSSM) of a rotor and a casing for the initial temperature and dynamic heating. The unique feature of the QPSSM of GTEs is separate equation sets, which allow the heat exchange between structure elements and the gas (air) and the displacements of the turbine rotor and the casing. This ability appears as a result of determining the effect of each factor on different structural elements of the engine. The presented method significantly simplifies the model identification, which can be performed based on a precise calculation of the unsteady temperature fields of the structural elements and the variation of the radial clearance. Thus, the present paper addresses a new method to model the engine dynamics considering its heating up. The method is based on the integration of three models: the gas-path dynamics model, the clearance dynamics model, and the model of the clearance effect on the efficiency. The paper also comprises the program implementation of the models. The method was tested by applying to a particular turbofan engine.