The article deals with simultaneous identification of heat transfer coefficient and ambient temperature. The general functional properties of thermal models are seeking for the unique estimation of two interrelated parameters. To substantiate the preservation of the one-to-one correspondence the simple approach is used. It is shown that the simultaneous identification of the heat transfer coefficient and ambient temperature is not possible unless the class of the functions to which they belong is suitably narrowed. Typical thermal models are considered and the narrowed classes of the sought properties are revealed. The idea can be applied for a wide class of inverse engineering problems.