Abstract <p>The ability to monitor the temperature of a medium bounded by walls without placing sensors directly in it is important for ensuring efficient operation of many devices and technological aggregates (heat treatment devices, engines, reactors, and others). However, the development of a monitoring process with a wide application field requires automation of the determination of thermophysical properties of the wall materials and medium without specialized testing, which is impeded by specific features of each object. Here, we report our results on the thermophysical properties of materials assessed by indirect monitoring of the temperature of a medium adjacent to a wall. We have examined difficulties encountered in attempts to automate determination of properties of materials via adaptation of models for complex heat exchange between the medium and wall with partially unknown properties. The use of simplified heat transfer models allowed us to represent model signals as increments relative to the initial instant of a time period and reduce the effect of the inconsistency of the functional form of the model with the object on indirect monitoring results. Parameters unknown during adaptation of the model were determined using retrospective data obtained in a limited time interval. The results demonstrate that the model can be used to monitor a generalized estimate of the ambient temperature near the place where the temperature in the wall is monitored, with subsequent prediction of consequences of varying the temperature of the isolated medium. The performance of the proposed approach has been illustrated by the example of an experiment in which a firebrick was heated. The results of this study can be useful in designing versatile temperature monitoring methods applicable to various objects.</p>