This paper focuses on the development of the criterion of optimality of transients of the control system, based on the minimum of exergy losses in the gas cooler of carbon dioxide heat pump. It is noted that the exergy quality criterion has a clear physical meaning, as compared with the integral quadratic criterion in which the choice of the coefficients in the integrand is not justified. Mathematic model of heat exchanger is obtained using the method of solving differential equations, without going to the irrational transfer functions. The model is reduced to transfer functions of the first and second order with the delay. The continuous temperature control system of heat pump gas cooler is considered. It is shown, that one of the versions of the control system for the minimization of the proposed criterion can be a combined control system using both the principle of the negative feedback and the principle of the invariance related to a number of disturbances affecting the processes of heat transfer in the heat exchanger.